Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
670 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 670 conjugacy classes of subgroups — too many to draw. Only its 117 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. C2×#11763042 | C2 | semidirect |
| 2. C2×#11762610 | C2 | semidirect |
| 3. C2×#11762588 | C2 | semidirect |
| 4. #14526876 | C2 | semidirect |
| 5. C22×C17×D16 | C2 | semidirect |
| 27. C2×D8×C17 | D4 | semidirect |
| 40. C2×C16×C17 | D4 | semidirect |
| 43. #10587489 | D4 | semidirect |
| 95. C22×D17 | D16 | semidirect |
| 117. C22×D16 | D17 | semidirect |
| 172. C2×D8 | C22⋊D17 | semidirect |
| 187. C2×C16 | C22⋊D17 | semidirect |
| 191. C17 | #13304 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#11763042 | 2 |
| C2×#11762610 | 2 |
| C2×#11762588 | 2 |
| #14526876 | 2 |
| C22×C17×D16 | 2 |
| #13304 | 17 |