Finite Group DatabasebetaFinite Group DatabasebetaOrder 5504.
936 conjugacy classes of subgroups; only the 285 normal subgroups are shown.
This group has 936 conjugacy classes of subgroups — too many to draw. Only its 285 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 | C22×C42×C43 | C2 |
| socle | C23×C43 | C24 |
| hypercenter | C22×C42 | D43 |
| hypocenter | C43 | #2297 |
| LCS | G ▷ C22×C43 ▷ C43 | |
| UCS | C1 ◁ C22×C4 ◁ C22×C42 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C2×#13063284 | C2 | semidirect |
| 3. #14582805 | C2 | semidirect |
| 4. #14582801 | C2 | semidirect |
| 5. #14582778 | C2 | semidirect |
| 6. C4×(C2×D43)⋊C4 | C2 | semidirect |
| 7. C22×C42×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 |
| 69. C2×C4×C43 | C22⋊C4 | semidirect |
| 76. C2×C4×C43 | #41 | semidirect |
| 112. C22×C42 | D43 | semidirect |
| 117. C43 | #2297 | semidirect |
| 188. C2×C4 | (C2×D43)⋊C4 | semidirect |
| 193. C2×C4 | #10621898 | semidirect |