Finite Group DatabasebetaFinite Group DatabasebetaOrder 3328.
2046 conjugacy classes of subgroups; only the 1152 normal subgroups are shown.
This group has 2046 conjugacy classes of subgroups — too many to draw. Only its 1152 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C43 | #261 |
| commutator, hypocenter | C13 | C2×C42×C8 |
| Frattini | C23 | C23×#261 |
| Fitting | C43×C13 | C4 |
| socle | C23×C13 | C23×C4 |
| prime radical | C23×D13 | C22×C4 |
| cosocle | C22×Dic13 | C24 |
| LCS | G ▷ C13 | |
| UCS | C1 ◁ C43 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C42×#1057 | C2 | semidirect |
| 8. C4×D13⋊C8 | C4 | direct (N × H) |
| 21. C42×D13 | C8 | semidirect |
| 23. C4×#1057 | C2×C4 | semidirect |
| 34. D13⋊C8 | C42 | direct (N × H) |
| 36. C42×C13 | C2×C8 | semidirect |
| 38. C4×Dic13 | C2×C8 | semidirect |
| 52. C4×D13 | C4×C8 | semidirect |
| 54. #1057 | C2×C42 | semidirect |
| 68. C4×C13 | C2×C4×C8 | semidirect |
| 69. Dic13 | C2×C4×C8 | semidirect |
| 85. D13 | C42×C8 | semidirect |
| 99. C42 | D13⋊C8 | direct (N × H) |
| 101. C13 | C2×C42×C8 | semidirect |
| 120. C4 | C4×D13⋊C8 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C4×D13⋊C8 | 2 |
| C42×#1057 | 2 |
| C43×D13 | 2 |
| C2×C42×C8 | 13 |