Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
370 conjugacy classes of subgroups; only the 109 normal subgroups are shown.
This group has 370 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 |
|---|---|---|
| 1. #11763412 | C2 | semidirect |
| 2. #11763111 | C2 | semidirect |
| 3. #11763108 | C2 | semidirect |
| 4. #11763062 | C2 | semidirect |
| 5. #11763043 | C2 | semidirect |
| 6. #11763003 | C2 | semidirect |
| 7. #11763002 | C2 | semidirect |
| 8. #11762837 | C2 | semidirect |
| 9. C17×#469 | C2 | semidirect |
| 109. #469 | D17 | semidirect |
| 144. C17 | #3259 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11763412 | 2 |
| #11763111 | 2 |
| #11763108 | 2 |
| #11763062 | 2 |
| #11763043 | 2 |
| #11763003 | 2 |
| #11763002 | 2 |
| #11762837 | 2 |
| C17×#469 | 2 |
| #3259 | 17 |