Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
686 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 686 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. #14538785 | C2 | semidirect |
| 2. #14538250 | C2 | semidirect |
| 3. #14533686 | C2 | semidirect |
| 4. #14527343 | C2 | semidirect |
| 5. #14527208 | C2 | semidirect |
| 6. #14527176 | C2 | semidirect |
| 7. C17×#1286 | C2 | semidirect |
| 58. #10587560 | D4 | semidirect |
| 69. #10587555 | D4 | semidirect |
| 72. C17×C4⋊C8 | D4 | semidirect |
| 74. C4×C8×C17 | D4 | semidirect |
| 113. C2×D68 | D8 | semidirect |
| 223. #1286 | D17 | semidirect |
| 330. C4⋊C8 | D68 | semidirect |
| 338. C4×C8 | D68 | semidirect |
| 342. C17 | #9996 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14538785 | 2 |
| #14538250 | 2 |
| #14533686 | 2 |
| #14527343 | 2 |
| #14527208 | 2 |
| #14527176 | 2 |
| C17×#1286 | 2 |
| #9996 | 17 |