Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
386 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 386 conjugacy classes of subgroups — too many to draw. Only its 123 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. #11763524 | C2 | semidirect |
| 2. #11763205 | C2 | semidirect |
| 3. #11763130 | C2 | semidirect |
| 4. #11763127 | C2 | semidirect |
| 5. #11763099 | C2 | semidirect |
| 6. #11763086 | C2 | semidirect |
| 7. #11763060 | C2 | semidirect |
| 8. C4×#63228 | C2 | semidirect |
| 9. #11762887 | C2 | semidirect |
| 10. #11762849 | C2 | semidirect |
| 11. C17×#547 | C2 | semidirect |
| 101. #3622 | #41 | semidirect |
| 123. #547 | D17 | semidirect |
| 168. C17 | #3354 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11763524 | 2 |
| #11763205 | 2 |
| #11763130 | 2 |
| #11763127 | 2 |
| #11763099 | 2 |
| #11763086 | 2 |
| #11763060 | 2 |
| C4×#63228 | 2 |
| #11762887 | 2 |
| #11762849 | 2 |
| C17×#547 | 2 |
| #3354 | 17 |