Finite Group DatabasebetaFinite Group DatabasebetaOrder 5504.
704 conjugacy classes of subgroups; only the 233 normal subgroups are shown.
This group has 704 conjugacy classes of subgroups — too many to draw. Only its 233 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C23 | C23×D43 |
| commutator | C22×C43 | C23×C4 |
| Fitting | C43×#382 | C2 |
| socle | C23×C43 | C24 |
| hypercenter | #382 | D43 |
| hypocenter | C43 | #2349 |
| LCS | G ▷ C22×C43 ▷ C43 | |
| UCS | C1 ◁ C23 ◁ #382 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 3. #14582795 | C2 | semidirect |
| 4. #14582773 | C2 | semidirect |
| 5. #14582758 | C2 | semidirect |
| 6. C4×C4⋊Dic43 | C2 | semidirect |
| 7. #95×D43 | C2 | semidirect |
| 8. C43×#382 | C2 | semidirect |
| 12. C4×D172 | C4 | semidirect |
| 42. C2×C4×D43 | C2×C4 | semidirect |
| 44. C42×C43 | C2×C4 | semidirect |
| 46. (C2×D43)⋊C4 | C2×C4 | semidirect |
| 48. C4⋊Dic43 | C2×C4 | semidirect |
| 75. D172 | C4⋊C4 | semidirect |
| 106. #382 | D43 | semidirect |
| 110. C43 | #2349 | semidirect |
| 152. C42 | C4×D43 | semidirect |