Finite Group DatabasebetaFinite Group DatabasebetaOrder 7552.
648 conjugacy classes of subgroups; only the 173 normal subgroups are shown.
This group has 648 conjugacy classes of subgroups — too many to draw. Only its 173 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C23 | C23×D59 |
| commutator | C22×C59 | C23×C4 |
| Fitting | C59×#386 | C2 |
| socle | C23×C59 | C24 |
| hypercenter | #386 | D59 |
| hypocenter | C59 | #2380 |
| LCS | G ▷ C22×C59 ▷ C59 | |
| UCS | C1 ◁ C23 ◁ #386 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. #16837282 | C2 | semidirect |
| 3. #16837281 | C2 | semidirect |
| 4. #16837280 | C2 | semidirect |
| 5. #16837279 | C2 | semidirect |
| 6. #16837278 | C2 | semidirect |
| 7. #16837278 | C2 | semidirect |
| 8. #16837269 | C2 | semidirect |
| 9. C59×#386 | C2 | semidirect |
| 15. #14273723 | C4 | semidirect |
| 37. C2×D4×C59 | C2×C4 | semidirect |
| 47. C2×C22⋊D59 | C2×C4 | semidirect |
| 48. C2×C22⋊D59 | C2×C4 | semidirect |
| 56. C2×D236 | C2×C4 | semidirect |
| 67. C4×Dic59 | C2×C4 | semidirect |
| 155. #386 | D59 | semidirect |
| 157. C59 | #2380 | semidirect |
| 194. C2×D4 | C4×D59 | semidirect |