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. #11763529 | C2 | semidirect |
| 3. #11763160 | C2 | semidirect |
| 4. #11763151 | C2 | semidirect |
| 5. #11763090 | C2 | semidirect |
| 6. #11763050 | C2 | semidirect |
| 7. #11763020 | C2 | semidirect |
| 8. #11762973 | C2 | semidirect |
| 9. C4×#63219 | C2 | semidirect |
| 10. #11762806 | C2 | semidirect |
| 11. C8×D4×C17 | C2 | semidirect |
| 130. C8×D4 | D17 | semidirect |
| 166. C17 | #3302 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11763529 | 2 |
| #11763464 | 2 |
| #11763160 | 2 |
| #11763151 | 2 |
| #11763090 | 2 |
| #11763050 | 2 |
| #11763020 | 2 |
| #11762973 | 2 |
| C4×#63219 | 2 |
| #11762806 | 2 |
| C8×D4×C17 | 2 |
| #3302 | 17 |