Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
350 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 350 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 |
|---|---|---|
| 2. Q8×Dic34 | C2 | semidirect |
| 3. #11763167 | C2 | semidirect |
| 5. #11763105 | C2 | semidirect |
| 6. #11763087 | C2 | semidirect |
| 7. #11763029 | C2 | semidirect |
| 8. #11762936 | C2 | semidirect |
| 9. #11762910 | 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 |
|---|---|
| #11763545 | 2 |
| Q8×Dic34 | 2 |
| #11763167 | 2 |
| #11763155 | 2 |
| #11763105 | 2 |
| #11763087 | 2 |
| #11763029 | 2 |
| #11762936 | 2 |
| #11762910 | 2 |
| C4×#63231 | 2 |
| C17×#460 | 2 |
| #3375 | 17 |