Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
278 conjugacy classes of subgroups; only the 55 normal subgroups are shown.
This group has 278 conjugacy classes of subgroups — too many to draw. Only its 55 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. #14541934 | C2 | semidirect |
| 2. #14531096 | C2 | semidirect |
| 3. C2×#11762648 | C2 | semidirect |
| 4. #14530905 | C2 | semidirect |
| 5. #14526976 | C2 | semidirect |
| 6. #14526925 | C2 | semidirect |
| 7. C17×#1417 | C2 | semidirect |
| 109. #1417 | D17 | semidirect |
| 170. C17 | #13670 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14541934 | 2 |
| #14531096 | 2 |
| C2×#11762648 | 2 |
| #14530905 | 2 |
| #14526976 | 2 |
| #14526925 | 2 |
| C17×#1417 | 2 |
| #13670 | 17 |