Finite Group DatabasebetaFinite Group DatabasebetaOrder 7552.
908 conjugacy classes of subgroups; only the 253 normal subgroups are shown.
This group has 908 conjugacy classes of subgroups — too many to draw. Only its 253 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 | C23×C59 | C24 |
| Frattini | C23 | C23×D59 |
| Fitting | C22×C4⋊C4×C59 | C2 |
| socle | C24×C59 | C23 |
| hypercenter | C22×C4⋊C4 | D59 |
| hypocenter | C59 | C2×#399 |
| LCS | G ▷ C23×C59 ▷ C59 | |
| UCS | C1 ◁ C24 ◁ C22×C4⋊C4 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C22×Dic59⋊C4 | C2 | semidirect |
| 4. #16837337 | C2 | direct (N × H) |
| 5. C2×C59⋊#95 | C2 | semidirect |
| 6. C22×C4⋊C4×C59 | C2 | semidirect |
| 11. C2×Dic59⋊C4 | C22 | semidirect |
| 16. C59⋊#95 | C22 | semidirect |
| 20. C2×C4⋊C4×C59 | C22 | semidirect |
| 97. C2×C59 | #399 | semidirect |
| 105. C22×C4⋊C4 | D59 | semidirect |
| 110. C59 | C2×#399 | semidirect |
| 119. C2×C4⋊C4 | C2×D59 | semidirect |
| 201. C2 | #16837337 | direct (N × H) |