Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
560 conjugacy classes of subgroups; only the 91 normal subgroups are shown.
This group has 560 conjugacy classes of subgroups — too many to draw. Only its 91 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. #14537812 | C2 | semidirect |
| 3. C4×#10587494 | C2 | semidirect |
| 4. #14527383 | C2 | semidirect |
| 5. #14527381 | C2 | semidirect |
| 6. #14526648 | C2 | semidirect |
| 7. C17×#1288 | C2 | semidirect |
| 63. C17×#97 | D4 | semidirect |
| 77. #10587474 | D4 | semidirect |
| 204. #1288 | D17 | semidirect |
| 308. #97 | D68 | semidirect |
| 317. C17 | #9187 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14537812 | 2 |
| #14534639 | 2 |
| C4×#10587494 | 2 |
| #14527383 | 2 |
| #14527381 | 2 |
| #14526648 | 2 |
| C17×#1288 | 2 |
| #9187 | 17 |