Finite Group DatabasebetaFinite Group DatabasebetaOrder 7552.
388 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 388 conjugacy classes of subgroups — too many to draw. Only its 125 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 | C2×C4×C59 | C24 |
| Frattini | C2×C4 | C23×D59 |
| Fitting | C59×#498 | C2 |
| socle | C22×C59 | C22×D4 |
| hypercenter | #498 | D59 |
| hypocenter | C59 | #3335 |
| LCS | G ▷ C2×C4×C59 ▷ C2×C59 ▷ C59 | |
| UCS | C1 ◁ C22 ◁ C42 ◁ #498 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #16838113 | C2 | semidirect |
| 3. #16837734 | C2 | semidirect |
| 4. #16837722 | C2 | semidirect |
| 5. #16837689 | C2 | semidirect |
| 6. #16837684 | C2 | semidirect |
| 7. #16837632 | C2 | semidirect |
| 8. C4×#11745660 | C2 | semidirect |
| 9. C8×D236 | C2 | semidirect |
| 10. #106×D59 | C2 | semidirect |
| 11. C59×#498 | C2 | semidirect |
| 90. D236 | SD16 | semidirect |
| 99. C8×C59 | #41 | semidirect |
| 126. #498 | D59 | semidirect |
| 135. C59 | #3335 | semidirect |
| 224. C8 | #11745689 | semidirect |