Finite Group DatabasebetaFinite Group DatabasebetaOrder 17536.
700 conjugacy classes of subgroups; only the 165 normal subgroups are shown.
This group has 700 conjugacy classes of subgroups — too many to draw. Only its 165 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 |
|---|---|---|
| 1. C2×#17984118 | C2 | semidirect |
| 2. C22×#14555500 | C2 | semidirect |
| 3. #22577974 | C2 | semidirect |
| 4. #22577565 | C2 | semidirect |
| 5. #22577559 | C2 | semidirect |
| 6. #22577412 | C2 | semidirect |
| 7. #22577399 | C2 | semidirect |
| 8. #22577370 | C2 | semidirect |
| 140. C137 | #3011 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#17984118 | 2 |
| C22×#14555500 | 2 |
| #22577974 | 2 |
| #22577565 | 2 |
| #22577559 | 2 |
| #22577412 | 2 |
| #22577399 | 2 |
| #22577370 | 2 |
| C2×2−1+4×C137 | 2 |
| #3011 | 137 |