Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
294 conjugacy classes of subgroups; only the 63 normal subgroups are shown.
This group has 294 conjugacy classes of subgroups — too many to draw. Only its 63 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. #14531096 | C2 | semidirect |
| 2. #14530887 | C2 | semidirect |
| 3. #14526971 | C2 | semidirect |
| 4. #14526924 | C2 | semidirect |
| 5. C17×#3414 | C2 | semidirect |
| 6. C2×D272 | C22 | semidirect |
| 10. #11762643 | C22 | semidirect |
| 11. #11762637 | C22 | semidirect |
| 31. C17×Q32 | D4 | semidirect |
| 35. C17×D16 | D4 | semidirect |
| 94. #3414 | D17 | semidirect |
| 142. Q32 | C22⋊D17 | semidirect |
| 147. D16 | C22⋊D17 | semidirect |
| 154. C17 | #13667 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14531096 | 2 |
| #14530887 | 2 |
| #14526971 | 2 |
| #14526924 | 2 |
| C17×#3414 | 2 |
| #13667 | 17 |