Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
416 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 416 conjugacy classes of subgroups — too many to draw. Only its 149 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. #11763101 | C2 | semidirect |
| 3. #11763096 | C2 | semidirect |
| 4. #11763091 | C2 | semidirect |
| 5. #11763086 | C2 | semidirect |
| 6. #11762849 | C2 | semidirect |
| 7. #11762833 | C2 | semidirect |
| 9. C2×C17×C4⋊Q8 | C2 | semidirect |
| 44. #63252 | Q8 | semidirect |
| 91. D68 | C2×Q8 | semidirect |
| 96. Dic34 | C2×Q8 | semidirect |
| 117. C2×C4⋊Q8 | D17 | semidirect |
| 156. C17 | #3079 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×#63252 | 2 |
| #11763101 | 2 |
| #11763096 | 2 |
| #11763091 | 2 |
| #11763086 | 2 |
| #11762849 | 2 |
| #11762833 | 2 |
| #11762808 | 2 |
| C2×C17×C4⋊Q8 | 2 |
| #3079 | 17 |