Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
632 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 632 conjugacy classes of subgroups — too many to draw. Only its 99 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. #14538793 | C2 | semidirect |
| 2. #14538583 | C2 | semidirect |
| 4. #14527347 | C2 | semidirect |
| 5. #14527208 | C2 | semidirect |
| 6. #14527176 | C2 | semidirect |
| 7. C17×#1286 | C2 | semidirect |
| 62. #10587555 | D4 | semidirect |
| 63. #10587555 | D4 | semidirect |
| 68. C17×C4⋊C8 | D4 | semidirect |
| 70. C4×C8×C17 | D4 | semidirect |
| 103. C2×D68 | SD16 | semidirect |
| 207. #1286 | D17 | semidirect |
| 309. C4⋊C8 | D68 | semidirect |
| 317. C4×C8 | D68 | semidirect |
| 321. C17 | #10000 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14538793 | 2 |
| #14538583 | 2 |
| #14533686 | 2 |
| #14527347 | 2 |
| #14527208 | 2 |
| #14527176 | 2 |
| C17×#1286 | 2 |
| #10000 | 17 |