Finite Group DatabasebetaFinite Group DatabasebetaOrder 7552.
484 conjugacy classes of subgroups; only the 175 normal subgroups are shown.
This group has 484 conjugacy classes of subgroups — too many to draw. Only its 175 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C22 | C2×D4×D59 |
| commutator | C4×C59 | C23×C4 |
| Frattini | C2×C4 | C23×D59 |
| Fitting | C59×#441 | C2 |
| socle | C22×C59 | C22×D4 |
| hypercenter | #441 | D59 |
| hypocenter | C59 | #2952 |
| LCS | G ▷ C4×C59 ▷ C2×C59 ▷ C59 | |
| UCS | C1 ◁ C22 ◁ C42 ◁ #441 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. #16837884 | C2 | semidirect |
| 3. #16837515 | C2 | semidirect |
| 4. #16837513 | C2 | semidirect |
| 5. #16837509 | C2 | semidirect |
| 6. C4×#11745671 | C2 | semidirect |
| 7. #16837487 | C2 | semidirect |
| 8. #106×D59 | C2 | semidirect |
| 9. #16837402 | C2 | semidirect |
| 10. #16837359 | C2 | semidirect |
| 11. C59×#441 | C2 | semidirect |
| 13. #14273750 | C4 | semidirect |
| 42. #11745689 | C2×C4 | semidirect |
| 50. Q16×C59 | C2×C4 | semidirect |
| 57. #11745671 | C2×C4 | semidirect |
| 69. D472 | C2×C4 | semidirect |
| 71. C8×D59 | C2×C4 | semidirect |
| 120. #441 | D59 | semidirect |
| 126. C59 | #2952 | semidirect |
| 165. Q16 | C4×D59 | semidirect |