Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
308 conjugacy classes of subgroups; only the 65 normal subgroups are shown.
This group has 308 conjugacy classes of subgroups — too many to draw. Only its 65 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. #14541740 | C2 | semidirect |
| 2. #14531025 | C2 | semidirect |
| 3. #14528265 | C2 | semidirect |
| 4. #14526835 | C2 | semidirect |
| 5. #14526765 | C2 | semidirect |
| 6. #14526751 | C2 | semidirect |
| 74. D8×C17 | SD16 | semidirect |
| 206. C17 | #12360 | semidirect |
| 221. D8 | #63229 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14541740 | 2 |
| #14531025 | 2 |
| #14528265 | 2 |
| #14526835 | 2 |
| #14526765 | 2 |
| #14526751 | 2 |
| C17×#2206 | 2 |
| #12360 | 17 |