Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
378 conjugacy classes of subgroups; only the 109 normal subgroups are shown.
This group has 378 conjugacy classes of subgroups — too many to draw. Only its 109 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. #11763153 | C2 | semidirect |
| 3. #11763148 | C2 | semidirect |
| 4. #11763067 | C2 | semidirect |
| 5. #11763048 | C2 | semidirect |
| 6. #11762966 | C2 | semidirect |
| 7. #11762963 | C2 | semidirect |
| 9. C17×#470 | C2 | semidirect |
| 111. #470 | D17 | semidirect |
| 145. C17 | #3202 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11763382 | 2 |
| #11763153 | 2 |
| #11763148 | 2 |
| #11763067 | 2 |
| #11763048 | 2 |
| #11762966 | 2 |
| #11762963 | 2 |
| #11762777 | 2 |
| C17×#470 | 2 |
| #3202 | 17 |