Finite Group DatabasebetaFinite Group DatabasebetaOrder 7552.
702 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 702 conjugacy classes of subgroups — too many to draw. Only its 149 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 | C22×C22⋊C4×C59 | C2 |
| hypercenter | C22×C22⋊C4 | D59 |
| hypocenter | C59 | #2622 |
| LCS | G ▷ C23×C59 ▷ C59 | |
| UCS | C1 ◁ C23 ◁ C22×C22⋊C4 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. #16837330 | C2 | semidirect |
| 3. #16837317 | C2 | semidirect |
| 4. #16837281 | C2 | semidirect |
| 5. #16837275 | C2 | semidirect |
| 6. #16837258 | C2 | semidirect |
| 7. C22×C22⋊C4×C59 | C2 | semidirect |
| 11. C2×Dic59⋊C4 | C22 | semidirect |
| 16. C2×(C2×D59)⋊C4 | C22 | semidirect |
| 17. C59⋊#95 | C22 | semidirect |
| 18. C59⋊#95 | C22 | semidirect |
| 99. C22×C22⋊C4 | D59 | semidirect |
| 105. C59 | #2622 | semidirect |