Finite Group DatabasebetaFinite Group DatabasebetaOrder 7552.
464 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 464 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×#399 | C2 |
| hypercenter | #399 | D59 |
| hypocenter | C59 | #2826 |
| LCS | G ▷ C23×C59 ▷ C59 | |
| UCS | C1 ◁ C23 ◁ #399 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #16837341 | C2 | semidirect |
| 2. #16837331 | C2 | semidirect |
| 3. #16837324 | C2 | semidirect |
| 4. #16837319 | C2 | semidirect |
| 5. #16837318 | C2 | semidirect |
| 7. #16837279 | C2 | semidirect |
| 8. #16837274 | C2 | semidirect |
| 9. C59×#399 | C2 | semidirect |
| 127. #399 | D59 | semidirect |
| 135. C59 | #2826 | semidirect |