Finite Group DatabasebetaFinite Group DatabasebetaOrder 7552.
540 conjugacy classes of subgroups; only the 189 normal subgroups are shown.
This group has 540 conjugacy classes of subgroups — too many to draw. Only its 189 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 | C59×#376 | C2 |
| socle | C23×C59 | C24 |
| hypercenter | #376 | D59 |
| hypocenter | C59 | #2319 |
| LCS | G ▷ C22×C59 ▷ C59 | |
| UCS | C1 ◁ C23 ◁ #376 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 3. #16837300 | C2 | semidirect |
| 4. #16837291 | C2 | semidirect |
| 5. #16837264 | C2 | semidirect |
| 6. #16837261 | C2 | semidirect |
| 7. C4×C4⋊Dic59 | C2 | semidirect |
| 8. C59×#376 | C2 | semidirect |
| 11. C4×D236 | C4 | semidirect |
| 104. #376 | D59 | semidirect |
| 105. C59 | #2319 | semidirect |