Finite Group DatabasebetaFinite Group DatabasebetaOrder 3328.
8094 conjugacy classes of subgroups; only the 4296 normal subgroups are shown.
This group has 8094 conjugacy classes of subgroups — too many to draw. Only its 4296 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C22×C42 | #261 |
| commutator, hypocenter | C13 | C22×C43 |
| Frattini | C22 | C24×#261 |
| Fitting | C22×C42×C13 | C4 |
| socle | C24×C13 | C22×C4 |
| prime radical | C24×D13 | C23 |
| cosocle | C22×D13 | C25 |
| LCS | G ▷ C13 | |
| UCS | C1 ◁ C22×C42 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C2×C42×#261 | C2 | direct (N × H) |
| 6. C22×C4×#261 | C4 | direct (N × H) |
| 8. C22×C42×C13 | C4 | semidirect |
| 9. C22×C4×Dic13 | C4 | semidirect |
| 10. C2×C42×D13 | C4 | semidirect |
| 12. C42×#261 | C22 | direct (N × H) |
| 21. C2×C4×#261 | C2×C4 | direct (N × H) |
| 23. C2×C42×C13 | C2×C4 | semidirect |
| 24. C2×C4×Dic13 | C2×C4 | semidirect |
| 25. C42×D13 | C2×C4 | semidirect |
| 32. C22×#261 | C42 | direct (N × H) |
| 35. C22×C4×C13 | C42 | semidirect |
| 37. C22×Dic13 | C42 | semidirect |
| 39. C2×C4×D13 | C42 | semidirect |
| 43. C4×#261 | C22×C4 | direct (N × H) |
| 44. C42×C13 | C22×C4 | semidirect |
| 45. C4×Dic13 | C22×C4 | semidirect |
| 56. C2×#261 | C2×C42 | direct (N × H) |
| 58. C2×C4×C13 | C2×C42 | semidirect |
| 60. C2×Dic13 | C2×C42 | semidirect |
| 62. C4×D13 | C2×C42 | semidirect |
| 71. C22×C42 | #261 | direct (N × H) |
| 73. C22×C13 | C43 | semidirect |
| 76. C2×D13 | C43 | semidirect |
| 80. #261 | C22×C42 | direct (N × H) |
| 81. C4×C13 | C22×C42 | semidirect |
| 82. Dic13 | C22×C42 | semidirect |
| 96. C2×C42 | C2×#261 | direct (N × H) |
| 97. C2×C13 | C2×C43 | semidirect |
| 99. D13 | C2×C43 | semidirect |
| 114. C22×C4 | C4×#261 | direct (N × H) |
| 118. C42 | C22×#261 | direct (N × H) |
| 119. C13 | C22×C43 | semidirect |
| 133. C2×C4 | C2×C4×#261 | direct (N × H) |
| 139. C22 | C42×#261 | direct (N × H) |
| 144. C4 | C22×C4×#261 | direct (N × H) |
| 147. C2 | C2×C42×#261 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×C4×#261 | 2 |
| C2×C42×#261 | 2 |
| C22×C42×D13 | 2 |
| C22×C43 | 13 |