Finite Group DatabasebetaFinite Group DatabasebetaOrder 7552.
480 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 480 conjugacy classes of subgroups — too many to draw. Only its 133 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C22 | C2×D4×D59 |
| commutator | C2×C4×C59 | C24 |
| Frattini | C2×C4 | C23×D59 |
| Fitting | C59×#461 | C2 |
| socle | C22×C59 | C22×D4 |
| hypercenter | #461 | D59 |
| hypocenter | C59 | #3039 |
| LCS | G ▷ C2×C4×C59 ▷ C2×C59 ▷ C59 | |
| UCS | C1 ◁ C22 ◁ C42 ◁ #461 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C4⋊Q8×D59 | C2 | semidirect |
| 4. #16837613 | C2 | semidirect |
| 5. #16837611 | C2 | semidirect |
| 6. #16837609 | C2 | semidirect |
| 7. #16837607 | C2 | semidirect |
| 8. #16837605 | C2 | semidirect |
| 9. #16837424 | C2 | semidirect |
| 10. #16837409 | C2 | semidirect |
| 11. C59×#461 | C2 | semidirect |
| 131. C4×C59 | #137 | semidirect |
| 139. Dic59 | #137 | semidirect |
| 154. #461 | D59 | semidirect |
| 157. C59 | #3039 | semidirect |
| 283. C4 | #14273756 | semidirect |