Finite Group DatabasebetaFinite Group DatabasebetaOrder 7552.
508 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 508 conjugacy classes of subgroups — too many to draw. Only its 117 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×#400 | C2 |
| hypercenter | #400 | D59 |
| hypocenter | C59 | #2828 |
| LCS | G ▷ C23×C59 ▷ C59 | |
| UCS | C1 ◁ C23 ◁ #400 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #16837331 | C2 | semidirect |
| 2. #16837320 | C2 | semidirect |
| 3. #16837319 | C2 | semidirect |
| 4. #16837319 | C2 | semidirect |
| 5. #16837312 | C2 | semidirect |
| 6. #16837312 | C2 | semidirect |
| 7. #16837303 | C2 | semidirect |
| 8. #16837291 | C2 | semidirect |
| 9. C59×#400 | C2 | semidirect |
| 135. #400 | D59 | semidirect |
| 144. C59 | #2828 | semidirect |