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. #11763103 | C2 | semidirect |
| 4. #11763097 | C2 | semidirect |
| 5. #11763095 | C2 | semidirect |
| 6. #11763091 | C2 | semidirect |
| 7. #11763089 | C2 | semidirect |
| 8. #11762850 | C2 | semidirect |
| 9. #11762831 | C2 | semidirect |
| 11. C17×#474 | C2 | semidirect |
| 51. #63254 | Q8 | semidirect |
| 86. D4×C17 | C2×Q8 | semidirect |
| 110. Dic34 | C2×Q8 | semidirect |
| 140. #474 | D17 | semidirect |
| 180. C17 | #3079 | semidirect |
| 229. D4 | 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×#63254 | 2 |
| #11763103 | 2 |
| #11763097 | 2 |
| #11763095 | 2 |
| #11763091 | 2 |
| #11763089 | 2 |
| #11762850 | 2 |
| #11762831 | 2 |
| #11762807 | 2 |
| C17×#474 | 2 |
| #3079 | 17 |