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 |
| 3. #11763159 | C2 | semidirect |
| 5. #11763094 | C2 | semidirect |
| 7. #11763016 | C2 | semidirect |
| 8. #11762940 | C2 | semidirect |
| 9. #11762914 | C2 | 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 |
| #11763168 | 2 |
| #11763159 | 2 |
| #11763099 | 2 |
| #11763094 | 2 |
| #11763028 | 2 |
| #11763016 | 2 |
| #11762940 | 2 |
| #11762914 | 2 |
| C4×#63229 | 2 |
| C17×#556 | 2 |
| #3369 | 17 |