Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
338 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 338 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. Q8×Dic34 | C2 | semidirect |
| 4. #11763159 | C2 | semidirect |
| 6. #11763092 | C2 | semidirect |
| 8. #11762936 | C2 | semidirect |
| 9. #11762916 | C2 | semidirect |
| 11. C17×#462 | C2 | semidirect |
| 120. #462 | 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 |
| #11763533 | 2 |
| #11763170 | 2 |
| #11763159 | 2 |
| #11763100 | 2 |
| #11763092 | 2 |
| #11763033 | 2 |
| #11762936 | 2 |
| #11762916 | 2 |
| C4×#63230 | 2 |
| C17×#462 | 2 |
| #3369 | 17 |