Finite Group DatabasebetaFinite Group DatabasebetaOrder 7552.
464 conjugacy classes of subgroups; only the 213 normal subgroups are shown.
This group has 464 conjugacy classes of subgroups — too many to draw. Only its 213 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 | C2×C22⋊Q8×C59 | C2 |
| socle | C23×C59 | C24 |
| hypercenter | C2×C22⋊Q8 | D59 |
| hypocenter | C59 | #2378 |
| LCS | G ▷ C22×C59 ▷ C59 | |
| UCS | C1 ◁ C23 ◁ C2×C22⋊Q8 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #16837309 | C2 | semidirect |
| 2. #16837301 | C2 | semidirect |
| 5. #16837288 | C2 | semidirect |
| 6. #16837288 | C2 | semidirect |
| 28. C22⋊Q8×C59 | C4 | semidirect |
| 120. C59 | #2378 | semidirect |
| 123. C22⋊Q8 | Dic59 | semidirect |