Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
492 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 492 conjugacy classes of subgroups — too many to draw. Only its 89 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 |
|---|---|---|
| 3. #14529728 | C2 | semidirect |
| 5. #14527334 | C2 | semidirect |
| 6. #14526639 | C2 | semidirect |
| 7. C17×#1288 | C2 | semidirect |
| 10. #11763203 | C4 | semidirect |
| 11. #11763169 | C4 | semidirect |
| 56. #10587555 | C2×C4 | semidirect |
| 57. #10587555 | C2×C4 | semidirect |
| 63. C17×#97 | C2×C4 | semidirect |
| 179. #1288 | D17 | semidirect |
| 272. #97 | C4×D17 | semidirect |
| 281. C17 | #9379 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14539789 | 2 |
| #14531594 | 2 |
| #14529728 | 2 |
| #14527381 | 2 |
| #14527334 | 2 |
| #14526639 | 2 |
| C17×#1288 | 2 |
| #9379 | 17 |