Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
222 conjugacy classes of subgroups; only the 87 normal subgroups are shown.
This group has 222 conjugacy classes of subgroups — too many to draw. Only its 87 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 |
|---|---|---|
| 3. #14526853 | C2 | semidirect |
| 4. Q8⋊#63214 | C2 | semidirect |
| 6. #14526703 | C2 | semidirect |
| 7. Q8×C16×C17 | C2 | semidirect |
| 71. Q8×C17 | M32 | semidirect |
| 90. Q8×C16 | D17 | semidirect |
| 149. C17 | #12056 | semidirect |
| 176. Q8 | #10587469 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14530617 | 2 |
| C8×#63230 | 2 |
| #14526853 | 2 |
| Q8⋊#63214 | 2 |
| #14526738 | 2 |
| #14526703 | 2 |
| Q8×C16×C17 | 2 |
| #12056 | 17 |