Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
704 conjugacy classes of subgroups; only the 165 normal subgroups are shown.
This group has 704 conjugacy classes of subgroups — too many to draw. Only its 165 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×#10587561 | C2 | semidirect |
| 3. C2×#10587561 | C2 | semidirect |
| 4. C2×C4×D68 | C2 | semidirect |
| 5. #11762726 | C2 | semidirect |
| 6. #11762715 | C2 | semidirect |
| 7. #11762711 | C2 | semidirect |
| 8. #11762687 | C2 | semidirect |
| 9. C4×C4⋊C4×C17 | C2 | semidirect |
| 57. C42×C17 | D4 | semidirect |
| 129. C4×C4⋊C4 | D17 | semidirect |
| 158. C17 | #2544 | semidirect |
| 191. C42 | D68 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#10587560 | 2 |
| C2×#10587561 | 2 |
| C2×C4×D68 | 2 |
| #11762726 | 2 |
| #11762715 | 2 |
| #11762711 | 2 |
| #11762687 | 2 |
| C4×C4⋊C4×C17 | 2 |
| #2544 | 17 |