Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
304 conjugacy classes of subgroups; only the 79 normal subgroups are shown.
This group has 304 conjugacy classes of subgroups — too many to draw. Only its 79 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 |
|---|---|---|
| 4. #14526842 | C2 | semidirect |
| 5. Q8⋊#63214 | C2 | semidirect |
| 6. #14526748 | C2 | semidirect |
| 7. Q8×Q16×C17 | C2 | semidirect |
| 61. Q16×C17 | SD16 | semidirect |
| 91. Q8×C17 | SD32 | semidirect |
| 110. Q8×Q16 | D17 | semidirect |
| 180. C17 | #12354 | semidirect |
| 189. Q16 | #63230 | semidirect |
| 218. Q8 | #10587499 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14531009 | 2 |
| #14530824 | 2 |
| #14528144 | 2 |
| #14526842 | 2 |
| Q8⋊#63214 | 2 |
| #14526748 | 2 |
| Q8×Q16×C17 | 2 |
| #12354 | 17 |