Finite Group DatabasebetaFinite Group DatabasebetaOrder 7552.
1840 conjugacy classes of subgroups; only the 725 normal subgroups are shown.
This group has 1840 conjugacy classes of subgroups — too many to draw. Only its 725 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C24 | C22×D59 |
| commutator | C22×C59 | C25 |
| Frattini | C22 | C24×D59 |
| Fitting | C24×C4×C59 | C2 |
| socle | C24×C59 | C23 |
| hypercenter | C24×C4 | D59 |
| hypocenter | C59 | C22×C22⋊Q8 |
| LCS | G ▷ C22×C59 ▷ C59 | |
| UCS | C1 ◁ C24 ◁ C24×C4 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C23×Dic118 | C2 | semidirect |
| 2. C2×#14273706 | C2 | direct (N × H) |
| 3. C22×C4⋊Dic59 | C2 | semidirect |
| 4. C22×Dic59⋊C4 | C2 | semidirect |
| 8. C22×Dic118 | C22 | semidirect |
| 11. #14273706 | C22 | direct (N × H) |
| 12. C2×C4⋊Dic59 | C22 | semidirect |
| 13. C2×Dic59⋊C4 | C22 | semidirect |
| 22. C24×C59 | Q8 | semidirect |
| 36. C2×Dic118 | C23 | semidirect |
| 38. C4⋊Dic59 | C23 | semidirect |
| 39. Dic59⋊C4 | C23 | semidirect |
| 45. C23×C59 | C2×Q8 | semidirect |
| 62. C22×C59 | C22⋊Q8 | semidirect |
| 65. C22×C59 | C22×Q8 | semidirect |
| 74. C2×C59 | C2×C22⋊Q8 | semidirect |
| 84. C59 | C22×C22⋊Q8 | semidirect |
| 100. C24 | Dic118 | semidirect |
| 122. C23 | C2×Dic118 | semidirect |
| 140. C22 | #14273706 | direct (N × H) |
| 143. C22 | C22×Dic118 | semidirect |
| 151. C2 | C2×#14273706 | direct (N × H) |