Finite Group DatabasebetaFinite Group DatabasebetaOrder 7552.
512 conjugacy classes of subgroups; only the 213 normal subgroups are shown.
This group has 512 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×#123×C59 | C2 |
| socle | C23×C59 | C24 |
| hypercenter | C2×#123 | D59 |
| hypocenter | C59 | #2376 |
| LCS | G ▷ C22×C59 ▷ C59 | |
| UCS | C1 ◁ C23 ◁ C2×#123 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. #16837301 | C2 | semidirect |
| 3. #16837295 | C2 | semidirect |
| 4. #16837295 | C2 | semidirect |
| 5. #16837288 | C2 | semidirect |
| 7. #16837277 | C2 | semidirect |
| 8. #16837262 | C2 | semidirect |
| 28. #123×C59 | C4 | semidirect |
| 39. C22×C4×C59 | C2×C4 | semidirect |
| 49. C4⋊C4×C59 | C2×C4 | semidirect |
| 51. C22⋊C4×C59 | C2×C4 | semidirect |
| 136. C59 | #2376 | semidirect |
| 140. #123 | Dic59 | semidirect |
| 172. C22×C4 | C2×Dic59 | semidirect |
| 180. C4⋊C4 | C2×Dic59 | semidirect |
| 186. C22⋊C4 | C2×Dic59 | semidirect |