Finite Group DatabasebetaFinite Group DatabasebetaOrder 7552.
532 conjugacy classes of subgroups; only the 137 normal subgroups are shown.
This group has 532 conjugacy classes of subgroups — too many to draw. Only its 137 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×#494 | C2 |
| socle | C22×C59 | C22×D4 |
| hypercenter | #494 | D59 |
| hypocenter | C59 | #3156 |
| LCS | G ▷ C2×C4×C59 ▷ C2×C59 ▷ C59 | |
| UCS | C1 ◁ C22 ◁ C42 ◁ #494 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×#14273759 | C2 | semidirect |
| 3. C2×Q16×D59 | C2 | semidirect |
| 4. #16837977 | C2 | semidirect |
| 5. #16837795 | C2 | semidirect |
| 6. #16837794 | C2 | semidirect |
| 7. #16837787 | C2 | semidirect |
| 8. #16837786 | C2 | semidirect |
| 9. #16837780 | C2 | semidirect |
| 10. #16837356 | C2 | semidirect |
| 11. C59×#494 | C2 | semidirect |
| 131. #494 | D59 | semidirect |
| 133. C59 | #3156 | semidirect |