Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
360 conjugacy classes of subgroups; only the 87 normal subgroups are shown.
This group has 360 conjugacy classes of subgroups — too many to draw. Only its 87 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. #14531041 | C2 | semidirect |
| 2. #14531034 | C2 | semidirect |
| 3. #14531033 | C2 | semidirect |
| 4. #14528398 | C2 | semidirect |
| 5. #14528391 | C2 | semidirect |
| 6. #14526700 | C2 | semidirect |
| 7. C17×#2248 | C2 | semidirect |
| 64. C16×C17 | D8 | semidirect |
| 65. #63214 | D8 | semidirect |
| 88. #2248 | D17 | semidirect |
| 145. C17 | #12519 | semidirect |
| 168. C16 | #63228 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14531041 | 2 |
| #14531034 | 2 |
| #14531033 | 2 |
| #14528398 | 2 |
| #14528391 | 2 |
| #14526700 | 2 |
| C17×#2248 | 2 |
| #12519 | 17 |