Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
1708 conjugacy classes of subgroups; only the 288 normal subgroups are shown.
This group has 1708 conjugacy classes of subgroups — too many to draw. Only its 288 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. C24×#3624 | C2 | semidirect |
| 2. C2×#11763840 | C2 | semidirect |
| 3. #14544757 | C2 | semidirect |
| 4. #14544728 | C2 | semidirect |
| 5. #14544606 | C2 | semidirect |
| 6. #14544521 | C2 | semidirect |
| 8. C22×#63247 | C22 | semidirect |
| 13. C2×#10587544 | C22 | semidirect |
| 16. C2×C22⋊#3624 | C22 | semidirect |
| 17. C2×#10587542 | C22 | semidirect |
| 18. #11763675 | C22 | semidirect |
| 38. C22×#3624 | D4 | semidirect |
| 60. C24×C17 | M16 | semidirect |
| 130. #3624 | #120 | semidirect |
| 146. C22×C17 | #435 | semidirect |
| 211. C17 | #21440 | semidirect |
| 214. C24 | #63247 | semidirect |
| 292. C22 | #11763840 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C24×#3624 | 2 |
| C2×#11763840 | 2 |
| #14544757 | 2 |
| #14544728 | 2 |
| #14544606 | 2 |
| #14544521 | 2 |
| #120×Dic17 | 2 |
| #21440 | 17 |