Finite Group DatabasebetaFinite Group DatabasebetaOrder 7552.
1056 conjugacy classes of subgroups; only the 173 normal subgroups are shown.
This group has 1056 conjugacy classes of subgroups — too many to draw. Only its 173 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 | C22×C22⋊C4×C59 | C2 |
| hypercenter | C22×C22⋊C4 | D59 |
| hypocenter | C59 | #2404 |
| LCS | G ▷ C23×C59 ▷ C59 | |
| UCS | C1 ◁ C23 ◁ C22×C22⋊C4 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C22×#11745685 | C2 | semidirect |
| 2. C2×#14273696 | C2 | semidirect |
| 3. #16837314 | C2 | semidirect |
| 4. #16837311 | C2 | semidirect |
| 5. #16837281 | C2 | semidirect |
| 6. #16837278 | C2 | semidirect |
| 7. #16837265 | C2 | semidirect |
| 8. C22×C22⋊C4×C59 | C2 | semidirect |
| 11. C22×Dic118 | C22 | semidirect |
| 12. C22×D236 | C22 | semidirect |
| 15. C22×C4×D59 | C22 | semidirect |
| 19. C2×(C2×D59)⋊C4 | C22 | semidirect |
| 20. C59⋊#95 | C22 | semidirect |
| 21. C59⋊#95 | C22 | semidirect |
| 22. C59⋊#95 | C22 | semidirect |
| 39. C22×C4×C59 | D4 | semidirect |
| 48. C2×C22⋊D59 | D4 | semidirect |
| 76. C23×C59 | #41 | semidirect |
| 136. C22×C22⋊C4 | D59 | semidirect |
| 142. C59 | #2404 | semidirect |
| 189. C22×C4 | C22⋊D59 | semidirect |
| 213. C23 | #11745685 | semidirect |