Finite Group DatabasebetaFinite Group DatabasebetaOrder 5504.
336 conjugacy classes of subgroups; only the 65 normal subgroups are shown.
This group has 336 conjugacy classes of subgroups — too many to draw. Only its 65 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C22 | #13063294 |
| commutator | C42×C43 | C23 |
| Frattini | C42 | C22×D43 |
| Fitting | D42×C43 | C2 |
| socle | C22×C43 | #120 |
| hypercenter | D42 | D43 |
| hypocenter | C43 | #1619 |
| LCS | G ▷ C42×C43 ▷ C22×C43 ▷ C43 | |
| UCS | C1 ◁ C22 ◁ C42 ◁ D42 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #14583275 | C2 | semidirect |
| 2. #14583094 | C2 | semidirect |
| 3. #14582643 | C2 | semidirect |
| 4. D4⋊(C43⋊C8) | C2 | semidirect |
| 5. D42×C43 | C2 | semidirect |
| 8. #13063322 | C22 | semidirect |
| 9. C4⋊(C43⋊C8) | C22 | semidirect |
| 11. C4×C43⋊C8 | C22 | semidirect |
| 45. D4×C43 | D8 | semidirect |
| 75. D42 | D43 | semidirect |
| 80. C43 | #1619 | semidirect |
| 123. D4 | #10621882 | semidirect |