Finite Group DatabasebetaFinite Group DatabasebetaOrder 7552.
484 conjugacy classes of subgroups; only the 189 normal subgroups are shown.
This group has 484 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 | C22 | C22×D236 |
| commutator | C4×C59 | C23×C4 |
| Frattini | C2×C4 | C23×D59 |
| Fitting | C59×#405 | C2 |
| socle | C22×C59 | C22×D4 |
| hypercenter | #405 | D59 |
| hypocenter | C59 | #2951 |
| LCS | G ▷ C4×C59 ▷ C2×C59 ▷ C59 | |
| UCS | C1 ◁ C22 ◁ #117 ◁ #405 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. #16837882 | C2 | semidirect |
| 3. #16837504 | C2 | semidirect |
| 4. C4×Dic236 | C2 | semidirect |
| 5. C4×D472 | C2 | semidirect |
| 6. C2×#14273661 | C2 | semidirect |
| 7. #16837404 | C2 | semidirect |
| 8. C59×#405 | C2 | semidirect |
| 10. #14273749 | C4 | semidirect |
| 33. #11745685 | C2×C4 | semidirect |
| 39. C2×C8×C59 | C2×C4 | semidirect |
| 52. Dic236 | C2×C4 | semidirect |
| 53. D472 | C2×C4 | semidirect |
| 54. #11745660 | C2×C4 | semidirect |
| 103. #405 | D59 | semidirect |
| 104. C59 | #2951 | semidirect |
| 138. C2×C8 | C4×D59 | semidirect |