Finite Group DatabasebetaFinite Group DatabasebetaOrder 5504.
188 conjugacy classes of subgroups; only the 57 normal subgroups are shown.
This group has 188 conjugacy classes of subgroups — too many to draw. Only its 57 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×#459 | C2 |
| socle | C22×C43 | #121 |
| hypercenter | #459 | D43 |
| hypocenter | C43 | #1665 |
| LCS | G ▷ C42×C43 ▷ C22×C43 ▷ C43 | |
| UCS | C1 ◁ C22 ◁ C42 ◁ #459 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #14583271 | C2 | semidirect |
| 2. #14583179 | C2 | semidirect |
| 3. D4×C43⋊C8 | C2 | semidirect |
| 4. #14582649 | C2 | semidirect |
| 5. #14582644 | C2 | semidirect |
| 6. #14582643 | C2 | semidirect |
| 51. D4×C43 | SD16 | semidirect |
| 65. C43⋊C8 | D8 | semidirect |
| 93. C43 | #1665 | semidirect |
| 139. D4 | #10621883 | semidirect |