Finite Group DatabasebetaFinite Group DatabasebetaOrder 7552.
5872 conjugacy classes of subgroups; only the 3221 normal subgroups are shown.
This group has 5872 conjugacy classes of subgroups — too many to draw. Only its 3221 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C23 | C23×D59 |
| commutator | C2×C59 | C26 |
| Frattini | C2 | C25×D59 |
| Fitting | C23×Q8×C59 | C2 |
| socle | C23×C59 | C24 |
| hypercenter | C23×Q8 | D59 |
| hypocenter | C59 | C22×2−1+4 |
| LCS | G ▷ C2×C59 ▷ C59 | |
| UCS | C1 ◁ C23 ◁ C23×Q8 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×#14273775 | C2 | direct (N × H) |
| 2. C22×#11745689 | C2 | semidirect |
| 3. C22×#11745685 | C2 | semidirect |
| 4. C22×Q8×D59 | C2 | semidirect |
| 5. C23×Q8×C59 | C2 | semidirect |
| 6. #14273775 | C22 | direct (N × H) |
| 7. C2×#11745689 | C22 | semidirect |
| 8. C2×#11745685 | C22 | semidirect |
| 10. C2×Q8×D59 | C22 | semidirect |
| 15. C22×Q8×C59 | C22 | semidirect |
| 20. C2×Q8×C59 | C23 | semidirect |
| 25. #11745689 | C23 | semidirect |
| 26. Q8×D59 | C23 | semidirect |
| 27. #11745685 | C23 | semidirect |
| 45. C22×C59 | 2−1+4 | semidirect |
| 54. C2×C59 | C2×2−1+4 | semidirect |
| 61. C23×Q8 | D59 | semidirect |
| 62. C59 | C22×2−1+4 | semidirect |
| 69. C22×Q8 | C2×D59 | semidirect |
| 81. C2×Q8 | C22×D59 | semidirect |
| 104. C22 | #14273775 | direct (N × H) |
| 111. C2 | C2×#14273775 | direct (N × H) |