Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
544 conjugacy classes of subgroups; only the 109 normal subgroups are shown.
This group has 544 conjugacy classes of subgroups — too many to draw. Only its 109 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 |
|---|---|---|
| 2. #14537503 | C2 | semidirect |
| 3. #14527434 | C2 | semidirect |
| 4. #14527209 | C2 | semidirect |
| 5. #14526681 | C2 | semidirect |
| 6. #14526629 | C2 | semidirect |
| 7. C17×#1955 | C2 | semidirect |
| 105. C2×C8×C17 | D8 | semidirect |
| 178. #1955 | D17 | semidirect |
| 280. C17 | #9049 | semidirect |
| 321. C2×C8 | #63228 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14538784 | 2 |
| #14537503 | 2 |
| #14527434 | 2 |
| #14527209 | 2 |
| #14526681 | 2 |
| #14526629 | 2 |
| C17×#1955 | 2 |
| #9049 | 17 |