Finite Group DatabasebetaFinite Group DatabasebetaOrder 5504.
370 conjugacy classes of subgroups; only the 129 normal subgroups are shown.
This group has 370 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.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #14583704 | C2 | semidirect |
| 2. #14583337 | C2 | semidirect |
| 3. #14583331 | C2 | semidirect |
| 4. C2×D688 | C2 | semidirect |
| 5. C43×#504 | C2 | semidirect |
| 8. #13063347 | C22 | semidirect |
| 9. C2×D344 | C22 | semidirect |
| 10. Dic344 | C22 | semidirect |
| 11. #13063270 | C22 | semidirect |
| 12. D688 | C22 | semidirect |
| 13. D688 | C22 | semidirect |
| 15. M32×C43 | C22 | semidirect |
| 16. C2×C16×C43 | C22 | semidirect |
| 55. #504 | D43 | semidirect |
| 56. C43 | #3415 | semidirect |
| 66. M32 | C2×D43 | semidirect |
| 67. C2×C16 | C2×D43 | semidirect |