Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
352 conjugacy classes of subgroups; only the 101 normal subgroups are shown.
This group has 352 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. #14530581 | C2 | semidirect |
| 3. #14530538 | C2 | semidirect |
| 4. Q8⋊#63214 | C2 | semidirect |
| 5. #14526740 | C2 | semidirect |
| 6. #14526738 | C2 | semidirect |
| 7. C17×Q8⋊C16 | C2 | semidirect |
| 106. Q8×C17 | M32 | semidirect |
| 118. D68 | M32 | semidirect |
| 139. Q8⋊C16 | D17 | semidirect |
| 218. C17 | #11623 | semidirect |
| 263. Q8 | #10587469 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C8×#63256 | 2 |
| #14530581 | 2 |
| #14530538 | 2 |
| Q8⋊#63214 | 2 |
| #14526740 | 2 |
| #14526738 | 2 |
| C17×Q8⋊C16 | 2 |
| #11623 | 17 |