Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
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×#10587637 | C2 | semidirect |
| 2. C22×#63231 | C2 | semidirect |
| 3. #11763380 | C2 | semidirect |
| 4. #11762971 | C2 | semidirect |
| 5. #11762965 | C2 | semidirect |
| 6. #11762818 | C2 | semidirect |
| 7. #11762805 | C2 | semidirect |
| 8. #11762776 | C2 | semidirect |
| 177. C17 | #3011 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#10587637 | 2 |
| C22×#63231 | 2 |
| #11763380 | 2 |
| #11762971 | 2 |
| #11762965 | 2 |
| #11762818 | 2 |
| #11762805 | 2 |
| #11762776 | 2 |
| C2×C17×2−1+4 | 2 |
| #3011 | 17 |