Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
836 conjugacy classes of subgroups; only the 173 normal subgroups are shown.
This group has 836 conjugacy classes of subgroups — too many to draw. Only its 173 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. C2×#10587633 | C2 | semidirect |
| 3. C2×#10587632 | C2 | semidirect |
| 4. #11762726 | C2 | semidirect |
| 5. #11762716 | C2 | semidirect |
| 6. #11762711 | C2 | semidirect |
| 7. #11762680 | C2 | semidirect |
| 8. C4×#63227 | C2 | semidirect |
| 9. C2×C17×C4⋊Q8 | C2 | semidirect |
| 94. C2×C4×C17 | #41 | semidirect |
| 131. C2×C4⋊Q8 | D17 | semidirect |
| 169. C17 | #2432 | semidirect |
| 241. C2×C4 | #63256 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#63256 | 2 |
| C2×#10587633 | 2 |
| C2×#10587632 | 2 |
| #11762726 | 2 |
| #11762716 | 2 |
| #11762711 | 2 |
| #11762680 | 2 |
| C4×#63227 | 2 |
| C2×C17×C4⋊Q8 | 2 |
| #2432 | 17 |