Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
416 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 416 conjugacy classes of subgroups — too many to draw. Only its 133 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. C4⋊Q8×D17 | C2 | semidirect |
| 3. #11763104 | C2 | semidirect |
| 4. #11763100 | C2 | semidirect |
| 5. #11763096 | C2 | semidirect |
| 6. #11763092 | C2 | semidirect |
| 7. #11763088 | C2 | semidirect |
| 8. #11762850 | C2 | semidirect |
| 9. #11762831 | C2 | semidirect |
| 11. C17×#477 | C2 | semidirect |
| 46. #63256 | Q8 | semidirect |
| 86. Q8×C17 | C2×Q8 | semidirect |
| 100. D68 | C2×Q8 | semidirect |
| 136. #477 | D17 | semidirect |
| 180. C17 | #3079 | semidirect |
| 226. Q8 | Q8×D17 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4⋊Q8×D17 | 2 |
| C4×#63256 | 2 |
| #11763104 | 2 |
| #11763100 | 2 |
| #11763096 | 2 |
| #11763092 | 2 |
| #11763088 | 2 |
| #11762850 | 2 |
| #11762831 | 2 |
| #11762809 | 2 |
| C17×#477 | 2 |
| #3079 | 17 |