Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
338 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 338 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. Q8×Dic34 | C2 | semidirect |
| 4. #11763160 | C2 | semidirect |
| 6. #11763095 | C2 | semidirect |
| 8. #11763020 | C2 | semidirect |
| 9. #11762917 | C2 | semidirect |
| 11. C17×#446 | C2 | semidirect |
| 121. #446 | D17 | semidirect |
| 157. C17 | #3369 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| Q8×Dic34 | 2 |
| #11763532 | 2 |
| #11763169 | 2 |
| #11763160 | 2 |
| #11763100 | 2 |
| #11763095 | 2 |
| #11763032 | 2 |
| #11763020 | 2 |
| #11762917 | 2 |
| C4×#63219 | 2 |
| C17×#446 | 2 |
| #3369 | 17 |