Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
678 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 678 conjugacy classes of subgroups — too many to draw. Only its 107 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. #14540091 | C2 | semidirect |
| 2. #14539699 | C2 | semidirect |
| 3. #14539236 | C2 | semidirect |
| 4. #14529711 | C2 | semidirect |
| 5. #14527278 | C2 | semidirect |
| 6. #14526635 | C2 | semidirect |
| 7. C17×#1980 | C2 | semidirect |
| 112. M16×C17 | D8 | semidirect |
| 191. #1980 | D17 | semidirect |
| 299. C17 | #10192 | semidirect |
| 337. M16 | #63228 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14540091 | 2 |
| #14539699 | 2 |
| #14539236 | 2 |
| #14529711 | 2 |
| #14527278 | 2 |
| #14526635 | 2 |
| C17×#1980 | 2 |
| #10192 | 17 |