Finite Group DatabasebetaFinite Group DatabasebetaOrder 5504.
332 conjugacy classes of subgroups; only the 79 normal subgroups are shown.
This group has 332 conjugacy classes of subgroups — too many to draw. Only its 79 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C4 | #13063293 |
| commutator | C2×C4×C43 | C22×C4 |
| Frattini | C22×C4 | C22×D43 |
| Fitting | C43×#421 | C2 |
| socle | C2×C43 | #386 |
| hypercenter | #421 | D43 |
| hypocenter | C43 | #1884 |
| LCS | G ▷ C2×C4×C43 ▷ C2×C43 ▷ C43 | |
| UCS | C1 ◁ C4 ◁ C22×C4 ◁ #421 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #14583665 | C2 | semidirect |
| 3. #14582916 | C2 | semidirect |
| 4. #14582872 | C2 | semidirect |
| 5. #14582660 | C2 | semidirect |
| 6. #14582658 | C2 | semidirect |
| 7. C43×#421 | C2 | semidirect |
| 13. #13063323 | C4 | semidirect |
| 14. #13063321 | C4 | semidirect |
| 15. #13063314 | C4 | semidirect |
| 16. #13063312 | C4 | semidirect |
| 47. M16×C43 | D4 | semidirect |
| 62. #10621877 | D4 | semidirect |
| 129. #421 | D43 | semidirect |
| 133. C43 | #1884 | semidirect |
| 176. M16 | C22⋊D43 | semidirect |