Finite Group DatabasebetaFinite Group DatabasebetaOrder 7552.
732 conjugacy classes of subgroups; only the 169 normal subgroups are shown.
This group has 732 conjugacy classes of subgroups — too many to draw. Only its 169 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 | C2×C4×D4×C59 | C2 |
| hypercenter | C2×C4×D4 | D59 |
| hypocenter | C59 | #2535 |
| LCS | G ▷ C23×C59 ▷ C59 | |
| UCS | C1 ◁ C23 ◁ C2×C4×D4 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×#14273698 | C2 | semidirect |
| 2. C2×C4×D236 | C2 | semidirect |
| 3. #16837327 | C2 | semidirect |
| 4. #16837311 | C2 | semidirect |
| 5. #16837281 | C2 | semidirect |
| 6. #16837268 | C2 | semidirect |
| 7. #16837259 | C2 | semidirect |
| 8. C2×C4×D4×C59 | C2 | semidirect |
| 32. C2×D4×C59 | D4 | semidirect |
| 51. C42×C59 | D4 | semidirect |
| 123. C2×C4×D4 | D59 | semidirect |
| 129. C59 | #2535 | semidirect |
| 158. C2×D4 | D236 | semidirect |
| 177. C42 | C22⋊D59 | semidirect |