Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
386 conjugacy classes of subgroups; only the 115 normal subgroups are shown.
This group has 386 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. C2×#10587630 | C2 | semidirect |
| 3. #11763200 | C2 | semidirect |
| 4. #11763176 | C2 | semidirect |
| 5. #11763018 | C2 | semidirect |
| 6. #11763012 | C2 | semidirect |
| 7. #11762967 | C2 | semidirect |
| 8. #11762965 | C2 | semidirect |
| 10. #11762863 | C2 | semidirect |
| 180. C17 | #3218 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#10587630 | 2 |
| #11763340 | 2 |
| #11763200 | 2 |
| #11763176 | 2 |
| #11763018 | 2 |
| #11763012 | 2 |
| #11762967 | 2 |
| #11762965 | 2 |
| #11762947 | 2 |
| #11762863 | 2 |
| C17×#448 | 2 |
| #3218 | 17 |