Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
622 conjugacy classes of subgroups; only the 101 normal subgroups are shown.
This group has 622 conjugacy classes of subgroups — too many to draw. Only its 101 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. #14533689 | C2 | semidirect |
| 3. #14527344 | C2 | semidirect |
| 4. #14527208 | C2 | semidirect |
| 5. #14527179 | C2 | semidirect |
| 6. #14526644 | C2 | semidirect |
| 7. C17×#3037 | C2 | semidirect |
| 97. C2×Q8×C17 | D8 | semidirect |
| 210. #3037 | D17 | semidirect |
| 329. C17 | #9997 | semidirect |
| 341. C2×Q8 | #63228 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14538780 | 2 |
| #14533689 | 2 |
| #14527344 | 2 |
| #14527208 | 2 |
| #14527179 | 2 |
| #14526644 | 2 |
| C17×#3037 | 2 |
| #9997 | 17 |