Finite Group DatabasebetaFinite Group DatabasebetaOrder 5504.
176 conjugacy classes of subgroups; only the 51 normal subgroups are shown.
This group has 176 conjugacy classes of subgroups — too many to draw. Only its 51 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C22 | #13063297 |
| commutator | C42×C43 | C23 |
| Frattini | C42 | C22×D43 |
| Fitting | C43×#461 | C2 |
| socle | C22×C43 | #121 |
| hypercenter | #461 | D43 |
| hypocenter | C43 | #1701 |
| LCS | G ▷ C42×C43 ▷ C22×C43 ▷ C43 | |
| UCS | C1 ◁ C22 ◁ C42 ◁ #461 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #14583247 | C2 | semidirect |
| 3. #14582977 | C2 | semidirect |
| 4. #14582649 | C2 | semidirect |
| 5. #14582645 | C2 | semidirect |
| 6. #14582642 | C2 | semidirect |
| 7. C43×#461 | C2 | semidirect |
| 86. #461 | D43 | semidirect |
| 92. C43 | #1701 | semidirect |