Finite Group DatabasebetaFinite Group DatabasebetaOrder 5504.
936 conjugacy classes of subgroups; only the 277 normal subgroups are shown.
This group has 936 conjugacy classes of subgroups — too many to draw. Only its 277 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C22×C4 | C22×D43 |
| commutator | C22×C43 | C23×C4 |
| Frattini | C23 | C23×D43 |
| Fitting | C2×#117×C43 | C2 |
| socle | C23×C43 | C24 |
| hypercenter | C2×#117 | D43 |
| hypocenter | C43 | #2297 |
| LCS | G ▷ C22×C43 ▷ C43 | |
| UCS | C1 ◁ C22×C4 ◁ C2×#117 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C22×C4×Dic43 | C2 | semidirect |
| 3. #14582804 | C2 | semidirect |
| 4. #14582800 | C2 | semidirect |
| 5. #14582776 | C2 | semidirect |
| 6. C4×(C2×D43)⋊C4 | C2 | semidirect |
| 7. C2×#117×C43 | C2 | semidirect |
| 10. C2×#10621898 | C4 | semidirect |
| 44. C2×D172 | C2×C4 | semidirect |
| 47. C2×C4×D43 | C2×C4 | semidirect |
| 50. C2×Dic86 | C2×C4 | semidirect |
| 68. C2×C4×C43 | C22⋊C4 | semidirect |
| 82. C2×Dic43 | #41 | semidirect |
| 111. C2×#117 | D43 | semidirect |
| 117. C43 | #2297 | semidirect |
| 189. C2×C4 | (C2×D43)⋊C4 | semidirect |