Finite Group DatabasebetaFinite Group DatabasebetaOrder 17536.
472 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 472 conjugacy classes of subgroups — too many to draw. Only its 141 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. #22577977 | C2 | semidirect |
| 3. #22577886 | C2 | semidirect |
| 4. #22577627 | C2 | semidirect |
| 5. #22577620 | C2 | semidirect |
| 6. #22577611 | C2 | semidirect |
| 7. #22577606 | C2 | semidirect |
| 8. #22577431 | C2 | semidirect |
| 9. #22577405 | C2 | semidirect |
| 10. C2×#17984012 | C2 | semidirect |
| 11. C2×#137×C137 | C2 | semidirect |
| 146. C137 | #3046 | semidirect |
| 148. C2×#137 | D137 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#17984108 | 2 |
| #22577977 | 2 |
| #22577886 | 2 |
| #22577627 | 2 |
| #22577620 | 2 |
| #22577611 | 2 |
| #22577606 | 2 |
| #22577431 | 2 |
| #22577405 | 2 |
| C2×#17984012 | 2 |
| C2×#137×C137 | 2 |
| #3046 | 137 |