Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
422 conjugacy classes of subgroups; only the 91 normal subgroups are shown.
This group has 422 conjugacy classes of subgroups — too many to draw. Only its 91 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. #14530557 | C2 | semidirect |
| 3. #14530534 | C2 | semidirect |
| 4. #14530513 | C2 | semidirect |
| 5. #14528822 | C2 | semidirect |
| 6. #14526899 | C2 | semidirect |
| 7. C17×#2112 | C2 | semidirect |
| 57. C2×C16×C17 | D4 | semidirect |
| 160. #2112 | D17 | semidirect |
| 238. C2×C16 | C22⋊D17 | semidirect |
| 248. C17 | #13395 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14538365 | 2 |
| #14530557 | 2 |
| #14530534 | 2 |
| #14530513 | 2 |
| #14528822 | 2 |
| #14526899 | 2 |
| C17×#2112 | 2 |
| #13395 | 17 |