Finite Group DatabasebetaFinite Group DatabasebetaOrder 7552.
398 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 398 conjugacy classes of subgroups — too many to draw. Only its 141 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×#424 | C2 |
| socle | C22×C59 | C22×D4 |
| hypercenter | #424 | D59 |
| hypocenter | C59 | #3081 |
| LCS | G ▷ C2×C4×C59 ▷ C2×C59 ▷ C59 | |
| UCS | C1 ◁ C22 ◁ #117 ◁ #424 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #16838030 | C2 | semidirect |
| 3. #16837703 | C2 | semidirect |
| 4. #16837703 | C2 | semidirect |
| 5. #16837693 | C2 | semidirect |
| 6. #16837683 | C2 | semidirect |
| 7. #16837444 | C2 | semidirect |
| 8. #16837440 | C2 | semidirect |
| 11. C59×#424 | C2 | semidirect |
| 13. #14273727 | C22 | semidirect |
| 15. #14273719 | 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. C4⋊C8×C59 | C22 | semidirect |
| 40. C4⋊C8×C59 | C22 | semidirect |
| 46. C2×D236 | Q8 | semidirect |
| 133. #424 | D59 | semidirect |
| 136. C59 | #3081 | semidirect |
| 160. C4⋊C8 | C2×D59 | semidirect |
| 161. C4⋊C8 | C2×D59 | semidirect |