Finite Group DatabasebetaFinite Group DatabasebetaOrder 7552.
1102 conjugacy classes of subgroups; only the 197 normal subgroups are shown.
This group has 1102 conjugacy classes of subgroups — too many to draw. Only its 197 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C23 | C23×D59 |
| commutator, socle | C23×C59 | C24 |
| Fitting | C2×#120×C59 | C2 |
| hypercenter | C2×#120 | D59 |
| hypocenter | C59 | #2849 |
| LCS | G ▷ C23×C59 ▷ C59 | |
| UCS | C1 ◁ C23 ◁ C2×#120 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C24×Dic59 | C2 | semidirect |
| 2. C2×#14273708 | C2 | semidirect |
| 3. #16837282 | C2 | semidirect |
| 4. #16837274 | C2 | semidirect |
| 5. #16837263 | C2 | semidirect |
| 6. #16837258 | C2 | semidirect |
| 13. C2×Dic59⋊C4 | C22 | semidirect |
| 16. C2×C22⋊Dic59 | C22 | semidirect |
| 17. C59⋊#95 | C22 | semidirect |
| 41. C22×Dic59 | D4 | semidirect |
| 87. C22×C59 | #123 | semidirect |
| 109. C59 | #2849 | semidirect |
| 189. C22 | #14273708 | semidirect |