Finite Group DatabasebetaFinite Group DatabasebetaOrder 7552.
476 conjugacy classes of subgroups; only the 213 normal subgroups are shown.
This group has 476 conjugacy classes of subgroups — too many to draw. Only its 213 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×#427 | C2 |
| socle | C22×C59 | C22×D4 |
| hypercenter | #427 | D59 |
| hypocenter | C59 | #2912 |
| LCS | G ▷ C4×C59 ▷ C2×C59 ▷ C59 | |
| UCS | C1 ◁ C22 ◁ C22×C4 ◁ #427 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 3. #16837445 | C2 | semidirect |
| 4. #16837443 | C2 | semidirect |
| 5. #16837437 | C2 | semidirect |
| 6. C2×#14273659 | C2 | semidirect |
| 7. #106×D59 | C2 | semidirect |
| 8. C59×#427 | C2 | semidirect |
| 10. #14273733 | C4 | semidirect |
| 38. C2×C8×C59 | C2×C4 | semidirect |
| 50. #11745664 | C2×C4 | semidirect |
| 52. #11745659 | C2×C4 | semidirect |
| 53. C8×D59 | C2×C4 | semidirect |
| 96. #427 | D59 | semidirect |
| 99. C59 | #2912 | semidirect |
| 133. C2×C8 | C4×D59 | semidirect |