Finite Group DatabasebetaFinite Group DatabasebetaOrder 5504.
396 conjugacy classes of subgroups; only the 129 normal subgroups are shown.
This group has 396 conjugacy classes of subgroups — too many to draw. Only its 129 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C23 | D4×D43 |
| commutator | C4×C43 | C2×C42 |
| Frattini | C22×C4 | C22×D43 |
| Fitting | C43×#340 | C2 |
| socle | C23×C43 | C2×D4 |
| hypercenter | #340 | D43 |
| hypocenter | C43 | C4×#102 |
| LCS | G ▷ C4×C43 ▷ C2×C43 ▷ C43 | |
| UCS | C1 ◁ C23 ◁ C22×C4 ◁ #340 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 4. C2×C8×Dic43 | C2 | semidirect |
| 5. C4⋊C4×Dic43 | C2 | semidirect |
| 6. #14582661 | C2 | semidirect |
| 7. C43×#340 | C2 | semidirect |
| 12. #13063287 | C4 | semidirect |
| 17. #13063247 | C4 | semidirect |
| 18. #13063245 | C4 | semidirect |
| 42. C2×C8×C43 | C2×C4 | semidirect |
| 46. C4⋊C4×C43 | C2×C4 | semidirect |
| 49. C4⋊Dic43 | C2×C4 | semidirect |
| 55. C2×C43⋊C8 | C2×C4 | semidirect |
| 88. D172 | C42 | semidirect |
| 114. Dic43 | #102 | semidirect |
| 130. #340 | D43 | semidirect |
| 131. C43 | C4×#102 | semidirect |
| 169. C2×C8 | C4×D43 | semidirect |
| 175. C4⋊C4 | C4×D43 | semidirect |