Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
348 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 348 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 |
|---|---|---|
| 3. #11763217 | C2 | semidirect |
| 4. #11763216 | C2 | semidirect |
| 5. #11763210 | C2 | semidirect |
| 6. #11763209 | C2 | semidirect |
| 50. M16×C17 | Q8 | semidirect |
| 78. #63223 | Q8 | semidirect |
| 167. C17 | #3166 | semidirect |
| 176. M16 | Dic34 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11763362 | 2 |
| C2×#10587576 | 2 |
| #11763217 | 2 |
| #11763216 | 2 |
| #11763210 | 2 |
| #11763209 | 2 |
| #11762852 | 2 |
| #11762851 | 2 |
| #11762849 | 2 |
| M16×Dic17 | 2 |
| C17×#428 | 2 |
| #3166 | 17 |