Finite Group DatabasebetaFinite Group DatabasebetaOrder 7552.
272 conjugacy classes of subgroups; only the 137 normal subgroups are shown.
This group has 272 conjugacy classes of subgroups — too many to draw. Only its 137 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22×C4 | C22×D59 |
| commutator | C22×C59 | C2×C42 |
| Fitting | C2×#97×C59 | C2 |
| socle | C23×C59 | C22×C4 |
| hypercenter | C2×#97 | D59 |
| hypocenter | C59 | #1770 |
| LCS | G ▷ C22×C59 ▷ C59 | |
| UCS | C1 ◁ C22×C4 ◁ C2×#97 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 13. Dic59⋊C8 | C4 | semidirect |
| 15. C8×Dic59 | C4 | semidirect |
| 63. C8×C59 | C4⋊C4 | semidirect |
| 78. Dic59 | #97 | semidirect |
| 92. C59 | #1770 | semidirect |
| 150. C8 | Dic59⋊C4 | semidirect |