Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
350 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 350 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 |
| 2. #11763168 | C2 | semidirect |
| 4. #11763104 | C2 | semidirect |
| 5. #11763089 | C2 | semidirect |
| 6. #11763028 | C2 | semidirect |
| 8. #11762940 | C2 | semidirect |
| 9. #11762909 | C2 | semidirect |
| 10. C4×#63231 | C2 | semidirect |
| 159. C17 | #3375 | 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 |
| #11763155 | 2 |
| #11763104 | 2 |
| #11763089 | 2 |
| #11763028 | 2 |
| #11763006 | 2 |
| #11762940 | 2 |
| #11762909 | 2 |
| C4×#63231 | 2 |
| C17×#559 | 2 |
| #3375 | 17 |