Finite Group DatabasebetaFinite Group DatabasebetaOrder 7552.
528 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 528 conjugacy classes of subgroups — too many to draw. Only its 149 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, socle | C23×C59 | C24 |
| Fitting | C59×#391 | C2 |
| hypercenter | #391 | D59 |
| hypocenter | C59 | #2732 |
| LCS | G ▷ C23×C59 ▷ C59 | |
| UCS | C1 ◁ C23 ◁ #391 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×#14273703 | C2 | semidirect |
| 2. #16837339 | C2 | semidirect |
| 3. #16837334 | C2 | semidirect |
| 4. #16837324 | C2 | semidirect |
| 6. #16837300 | C2 | semidirect |
| 8. #16837276 | C2 | semidirect |
| 9. C59×#391 | C2 | semidirect |
| 35. C2×Q8×C59 | D4 | semidirect |
| 46. C2×D236 | Q8 | semidirect |
| 134. #391 | D59 | semidirect |
| 139. C59 | #2732 | semidirect |
| 165. C2×Q8 | D236 | semidirect |