Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
396 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 396 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. #11763359 | C2 | semidirect |
| 2. #11763343 | C2 | semidirect |
| 3. #11763203 | C2 | semidirect |
| 4. #11763198 | C2 | semidirect |
| 5. #11763178 | C2 | semidirect |
| 6. #11763174 | C2 | semidirect |
| 7. #11763032 | C2 | semidirect |
| 8. #11763025 | C2 | semidirect |
| 9. #11762973 | C2 | semidirect |
| 10. #11762956 | C2 | semidirect |
| 11. C17×#432 | C2 | semidirect |
| 145. #432 | D17 | semidirect |
| 183. C17 | #3219 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11763359 | 2 |
| #11763343 | 2 |
| #11763203 | 2 |
| #11763198 | 2 |
| #11763178 | 2 |
| #11763174 | 2 |
| #11763032 | 2 |
| #11763025 | 2 |
| #11762973 | 2 |
| #11762956 | 2 |
| C17×#432 | 2 |
| #3219 | 17 |