Finite Group DatabasebetaFinite Group DatabasebetaOrder 7552.
418 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 418 conjugacy classes of subgroups — too many to draw. Only its 133 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C22 | C22×D236 |
| commutator | C2×C4×C59 | C24 |
| Frattini | C2×C4 | C23×D59 |
| Fitting | C59×#408 | C2 |
| socle | C22×C59 | C22×D4 |
| hypercenter | #408 | D59 |
| hypocenter | C59 | #3096 |
| LCS | G ▷ C2×C4×C59 ▷ C2×C59 ▷ C59 | |
| UCS | C1 ◁ C22 ◁ C2×#41 ◁ #408 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. #16837885 | C2 | semidirect |
| 3. #16837727 | C2 | semidirect |
| 4. #16837727 | C2 | semidirect |
| 5. #16837721 | C2 | semidirect |
| 6. #16837716 | C2 | semidirect |
| 7. #16837444 | C2 | semidirect |
| 8. #16837440 | C2 | semidirect |
| 9. #16837408 | C2 | semidirect |
| 10. C2×#14273649 | C2 | semidirect |
| 11. C59×#408 | C2 | semidirect |
| 23. #14273686 | C22 | semidirect |
| 25. C2×C4⋊Dic59 | C22 | semidirect |
| 26. #14273661 | C22 | semidirect |
| 27. #14273661 | C22 | semidirect |
| 28. #14273661 | C22 | semidirect |
| 29. #14273659 | C22 | semidirect |
| 30. #14273659 | C22 | semidirect |
| 31. #14273659 | C22 | semidirect |
| 39. C22⋊C8×C59 | C22 | semidirect |
| 40. C22⋊C8×C59 | C22 | semidirect |
| 145. #408 | D59 | semidirect |
| 146. C59 | #3096 | semidirect |
| 174. C22⋊C8 | C2×D59 | semidirect |
| 175. C22⋊C8 | C2×D59 | semidirect |