Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
362 conjugacy classes of subgroups; only the 115 normal subgroups are shown.
This group has 362 conjugacy classes of subgroups — too many to draw. Only its 115 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. #11763432 | C2 | semidirect |
| 2. #11763206 | C2 | semidirect |
| 3. #11763194 | C2 | semidirect |
| 4. #11763170 | C2 | semidirect |
| 6. #11763040 | C2 | semidirect |
| 7. #11762920 | C2 | semidirect |
| 8. #11762916 | C2 | semidirect |
| 9. #11762894 | C2 | semidirect |
| 10. #11762767 | C2 | semidirect |
| 11. C17×#470 | C2 | semidirect |
| 110. #470 | D17 | semidirect |
| 148. C17 | #3173 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11763432 | 2 |
| #11763206 | 2 |
| #11763194 | 2 |
| #11763170 | 2 |
| #11763062 | 2 |
| #11763040 | 2 |
| #11762920 | 2 |
| #11762916 | 2 |
| #11762894 | 2 |
| #11762767 | 2 |
| C17×#470 | 2 |
| #3173 | 17 |