Finite Group DatabasebetaFinite Group DatabasebetaOrder 3328.
2590 conjugacy classes of subgroups; only the 1515 normal subgroups are shown.
This group has 2590 conjugacy classes of subgroups — too many to draw. Only its 1515 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C23×C16 | D13 |
| commutator, hypocenter | C13 | C24×C16 |
| Frattini | C8 | C24×D13 |
| Fitting | C23×C13×C16 | C2 |
| socle | C24×C13 | C2×C8 |
| prime radical | C24×D13 | C8 |
| cosocle | C8×C13 | C25 |
| LCS | G ▷ C13 | |
| UCS | C1 ◁ C23×C16 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C23×#6090 | C2 | semidirect |
| 3. C22×C16×D13 | C2 | direct (N × H) |
| 4. C23×C13×C16 | C2 | semidirect |
| 10. C22×C13×C16 | C22 | semidirect |
| 11. C22×#6090 | C22 | semidirect |
| 12. C2×C16×D13 | C22 | direct (N × H) |
| 23. C2×C13×C16 | C23 | semidirect |
| 24. C2×#6090 | C23 | semidirect |
| 25. C16×D13 | C23 | direct (N × H) |
| 28. C23×D13 | C16 | direct (N × H) |
| 40. C13×C16 | C24 | semidirect |
| 41. #6090 | C24 | semidirect |
| 45. C23×C16 | D13 | direct (N × H) |
| 46. C23×C13 | C2×C16 | semidirect |
| 48. C22×D13 | C2×C16 | direct (N × H) |
| 65. C22×C16 | C2×D13 | direct (N × H) |
| 66. C22×C13 | C22×C16 | semidirect |
| 68. C2×D13 | C22×C16 | direct (N × H) |
| 85. C2×C16 | C22×D13 | direct (N × H) |
| 86. C2×C13 | C23×C16 | semidirect |
| 88. D13 | C23×C16 | direct (N × H) |
| 103. C16 | C23×D13 | direct (N × H) |
| 104. C13 | C24×C16 | semidirect |
| 107. C23 | C16×D13 | direct (N × H) |
| 119. C22 | C2×C16×D13 | direct (N × H) |
| 125. C2 | C22×C16×D13 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×C8×D13 | 2 |
| C23×#6090 | 2 |
| C22×C16×D13 | 2 |
| C23×C13×C16 | 2 |
| C24×C16 | 13 |