Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
324 conjugacy classes of subgroups; only the 78 normal subgroups are shown.
This group has 324 conjugacy classes of subgroups — too many to draw. Only its 78 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 |
|---|---|---|
| 2. C2×#11763696 | C2 | semidirect |
| 4. #14544892 | C2 | semidirect |
| 5. #14543845 | C2 | semidirect |
| 6. #14543844 | C2 | semidirect |
| 21. #11762613 | C4 | semidirect |
| 22. #11762611 | C4 | semidirect |
| 23. #11762609 | C4 | semidirect |
| 24. C17×#358 | C4 | semidirect |
| 167. #358 | #595 | semidirect |
| 213. C17 | #13152 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#11763724 | 2 |
| C2×#11763696 | 2 |
| #14544935 | 2 |
| #14544892 | 2 |
| #14543845 | 2 |
| #14543844 | 2 |
| #14530490 | 2 |
| #13152 | 17 |