Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
388 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 388 conjugacy classes of subgroups — too many to draw. Only its 117 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. #11763385 | C2 | semidirect |
| 2. #11763196 | C2 | semidirect |
| 3. #11763181 | C2 | semidirect |
| 4. #11763179 | C2 | semidirect |
| 5. #11763166 | C2 | semidirect |
| 6. #11763024 | C2 | semidirect |
| 7. #11763014 | C2 | semidirect |
| 8. #11762952 | C2 | semidirect |
| 9. #11762947 | C2 | semidirect |
| 10. #11762870 | C2 | semidirect |
| 11. C17×#540 | C2 | semidirect |
| 116. #540 | D17 | semidirect |
| 159. C17 | #3221 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11763385 | 2 |
| #11763196 | 2 |
| #11763181 | 2 |
| #11763179 | 2 |
| #11763166 | 2 |
| #11763024 | 2 |
| #11763014 | 2 |
| #11762952 | 2 |
| #11762947 | 2 |
| #11762870 | 2 |
| C17×#540 | 2 |
| #3221 | 17 |