Finite Group DatabasebetaFinite Group DatabasebetaOrder 7552.
396 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 396 conjugacy classes of subgroups — too many to draw. Only its 117 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×#459 | C2 |
| socle | C22×C59 | C22×D4 |
| hypercenter | #459 | D59 |
| hypocenter | C59 | #3366 |
| LCS | G ▷ C2×C4×C59 ▷ C2×C59 ▷ C59 | |
| UCS | C1 ◁ C22 ◁ C42 ◁ #459 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #16838109 | C2 | semidirect |
| 2. #16838072 | C2 | semidirect |
| 3. #16837765 | C2 | semidirect |
| 4. #16837748 | C2 | semidirect |
| 5. #16837704 | C2 | semidirect |
| 6. #16837693 | C2 | semidirect |
| 7. #16837595 | C2 | semidirect |
| 8. #16837529 | C2 | semidirect |
| 9. #16837514 | C2 | semidirect |
| 10. C4×#11745669 | C2 | semidirect |
| 11. C59×#459 | C2 | semidirect |
| 82. D4×C59 | #41 | semidirect |
| 137. #459 | D59 | semidirect |
| 141. C59 | #3366 | semidirect |
| 218. D4 | #11745687 | semidirect |