Finite Group DatabasebetaFinite Group DatabasebetaOrder 7552.
774 conjugacy classes of subgroups; only the 297 normal subgroups are shown.
This group has 774 conjugacy classes of subgroups — too many to draw. Only its 297 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C2×C4 | C23×D59 |
| commutator, socle | C22×C59 | C23×C4 |
| Fitting | C22×#41×C59 | C2 |
| hypercenter | C22×#41 | D59 |
| hypocenter | C59 | #2880 |
| LCS | G ▷ C22×C59 ▷ C59 | |
| UCS | C1 ◁ C2×C4 ◁ C22×#41 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×#14273734 | C2 | semidirect |
| 2. #16837369 | C2 | semidirect |
| 3. #16837366 | C2 | semidirect |
| 4. C2×C22⋊(C59⋊C8) | C2 | semidirect |
| 7. C2×#11745664 | C22 | semidirect |
| 8. C22×C59⋊C8 | C22 | semidirect |
| 11. C22⋊(C59⋊C8) | C22 | semidirect |
| 12. C22⋊(C59⋊C8) | C22 | semidirect |
| 76. C22×C59 | #131 | semidirect |
| 94. C59 | #2880 | semidirect |
| 165. C22 | #14273734 | semidirect |