Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
578 conjugacy classes of subgroups; only the 81 normal subgroups are shown.
This group has 578 conjugacy classes of subgroups — too many to draw. Only its 81 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. #14539775 | C2 | semidirect |
| 2. #14539771 | C2 | semidirect |
| 3. #14527253 | C2 | semidirect |
| 4. #14527202 | C2 | semidirect |
| 5. #14527136 | C2 | semidirect |
| 6. #14526656 | C2 | semidirect |
| 7. C17×#3153 | C2 | semidirect |
| 185. #3153 | D17 | semidirect |
| 296. C17 | #10120 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14539775 | 2 |
| #14539771 | 2 |
| #14527253 | 2 |
| #14527202 | 2 |
| #14527136 | 2 |
| #14526656 | 2 |
| C17×#3153 | 2 |
| #10120 | 17 |