Finite Group DatabasebetaFinite Group DatabasebetaOrder 5504.
336 conjugacy classes of subgroups; only the 59 normal subgroups are shown.
This group has 336 conjugacy classes of subgroups — too many to draw. Only its 59 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C22 | #13063293 |
| commutator | C42×C43 | C23 |
| Frattini | C42 | C22×D43 |
| Fitting | C43×#459 | C2 |
| socle | C22×C43 | #120 |
| hypercenter | #459 | D43 |
| hypocenter | C43 | #1619 |
| 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. D4×D172 | C2 | semidirect |
| 2. #14583275 | C2 | semidirect |
| 3. #14583091 | C2 | semidirect |
| 4. #14582642 | C2 | semidirect |
| 5. D4⋊(C43⋊C8) | C2 | semidirect |
| 6. #14582626 | C2 | semidirect |
| 7. C43×#459 | C2 | semidirect |
| 17. C4⋊(C43⋊C8) | C22 | semidirect |
| 19. C4×C43⋊C8 | C22 | semidirect |
| 21. #127×C43 | C22 | semidirect |
| 23. C4⋊C8×C43 | C22 | semidirect |
| 67. D4×C43 | D8 | semidirect |
| 83. D172 | D8 | semidirect |
| 121. #459 | D43 | semidirect |
| 125. C43 | #1619 | semidirect |
| 132. #127 | C2×D43 | semidirect |
| 139. C4⋊C8 | C2×D43 | semidirect |
| 194. D4 | #10621882 | semidirect |