Finite Group DatabasebetaFinite Group DatabasebetaOrder 5504.
380 conjugacy classes of subgroups; only the 71 normal subgroups are shown.
This group has 380 conjugacy classes of subgroups — too many to draw. Only its 71 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C2 | #14582807 |
| commutator | C22×C4×C43 | C23 |
| Frattini | C22×C4 | C22×D43 |
| Fitting | C43×#575 | C2 |
| socle | C2×C43 | #392 |
| hypercenter | #575 | D43 |
| hypocenter | C43 | #2008 |
| LCS | G ▷ C22×C4×C43 ▷ C2×C43 ▷ C43 | |
| UCS | C1 ◁ C2 ◁ C22×C4 ◁ #575 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×#13063350 | C2 | semidirect |
| 2. #14583463 | C2 | semidirect |
| 3. #14582916 | C2 | semidirect |
| 4. #14582905 | C2 | semidirect |
| 5. #14582873 | C2 | semidirect |
| 6. #14582670 | C2 | semidirect |
| 7. C43×#575 | C2 | semidirect |
| 41. C2×Q8×C43 | D4 | semidirect |
| 45. C2×D4×C43 | D4 | semidirect |
| 62. C2×C8×C43 | D4 | semidirect |
| 73. #10621877 | D4 | semidirect |
| 143. #575 | D43 | semidirect |
| 150. C43 | #2008 | semidirect |
| 184. C2×Q8 | C22⋊D43 | semidirect |
| 195. C2×D4 | C22⋊D43 | semidirect |
| 210. C2×C8 | C22⋊D43 | semidirect |