Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
1068 conjugacy classes of subgroups; only the 163 normal subgroups are shown.
This group has 1068 conjugacy classes of subgroups — too many to draw. Only its 163 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. C2×#11763545 | C2 | semidirect |
| 2. #14538902 | C2 | semidirect |
| 3. #14527903 | C2 | semidirect |
| 4. #14527841 | C2 | semidirect |
| 5. #14527498 | C2 | semidirect |
| 6. #14527232 | C2 | semidirect |
| 16. #11763101 | C22 | semidirect |
| 17. #11763006 | C22 | semidirect |
| 22. #11762541 | C22 | semidirect |
| 236. C17 | #18526 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#11763545 | 2 |
| #14538902 | 2 |
| #14527903 | 2 |
| #14527841 | 2 |
| #14527498 | 2 |
| #14527232 | 2 |
| C17×#3151 | 2 |
| #18526 | 17 |