Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
424 conjugacy classes of subgroups; only the 121 normal subgroups are shown.
This group has 424 conjugacy classes of subgroups — too many to draw. Only its 121 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. C4⋊Q8×D17 | C2 | semidirect |
| 3. #11763171 | C2 | semidirect |
| 4. #11763169 | C2 | semidirect |
| 5. #11763168 | C2 | semidirect |
| 6. #11763158 | C2 | semidirect |
| 7. #11763154 | C2 | semidirect |
| 8. #11762809 | C2 | semidirect |
| 9. #11762807 | C2 | semidirect |
| 10. #11762761 | C2 | semidirect |
| 11. C17×#489 | C2 | semidirect |
| 140. #489 | D17 | semidirect |
| 183. C17 | #3141 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11763358 | 2 |
| C4⋊Q8×D17 | 2 |
| #11763171 | 2 |
| #11763169 | 2 |
| #11763168 | 2 |
| #11763158 | 2 |
| #11763154 | 2 |
| #11762809 | 2 |
| #11762807 | 2 |
| #11762761 | 2 |
| C17×#489 | 2 |
| #3141 | 17 |