Finite Group DatabasebetaFinite Group DatabasebetaOrder 17536.
340 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 340 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. #22577800 | C2 | semidirect |
| 44. C2×#11764040 | Q8 | semidirect |
| 65. M16×C137 | Q8 | semidirect |
| 112. C137 | #3163 | semidirect |
| 159. M16 | Dic274 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22578034 | 2 |
| #22578031 | 2 |
| #22577811 | 2 |
| #22577810 | 2 |
| #22577804 | 2 |
| #22577800 | 2 |
| #22577445 | 2 |
| #22577439 | 2 |
| C2×#17984019 | 2 |
| #22577361 | 2 |
| #428×C137 | 2 |
| #3163 | 137 |