Finite Group DatabasebetaFinite Group DatabasebetaOrder 17536.
348 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 348 conjugacy classes of subgroups — too many to draw. Only its 149 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. #22577811 | C2 | semidirect |
| 4. #22577810 | C2 | semidirect |
| 5. #22577804 | C2 | semidirect |
| 6. #22577803 | C2 | semidirect |
| 48. #14555494 | Q8 | semidirect |
| 72. M16×C137 | Q8 | semidirect |
| 124. C137 | #3166 | semidirect |
| 176. M16 | Dic274 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22577956 | 2 |
| C2×#17984079 | 2 |
| #22577811 | 2 |
| #22577810 | 2 |
| #22577804 | 2 |
| #22577803 | 2 |
| #22577446 | 2 |
| #22577445 | 2 |
| #22577443 | 2 |
| M16×Dic137 | 2 |
| #428×C137 | 2 |
| #3166 | 137 |