Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
386 conjugacy classes of subgroups; only the 121 normal subgroups are shown.
This group has 386 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. C2×Q8×Dic17 | C2 | semidirect |
| 3. #11763142 | C2 | semidirect |
| 5. #11763114 | C2 | semidirect |
| 6. #11763033 | C2 | semidirect |
| 8. #11762916 | C2 | semidirect |
| 9. #11762912 | C2 | semidirect |
| 10. #11762863 | C2 | semidirect |
| 11. C17×#451 | C2 | semidirect |
| 133. #451 | D17 | semidirect |
| 174. C17 | #3117 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11763345 | 2 |
| C2×Q8×Dic17 | 2 |
| #11763142 | 2 |
| #11763128 | 2 |
| #11763114 | 2 |
| #11763033 | 2 |
| #11762948 | 2 |
| #11762916 | 2 |
| #11762912 | 2 |
| #11762863 | 2 |
| C17×#451 | 2 |
| #3117 | 17 |