Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
534 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 534 conjugacy classes of subgroups — too many to draw. Only its 141 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. C2×#10587562 | C2 | semidirect |
| 2. C2×#10587561 | C2 | semidirect |
| 3. #11762731 | C2 | semidirect |
| 4. #11762730 | C2 | semidirect |
| 5. #11762727 | C2 | semidirect |
| 6. #11762726 | C2 | semidirect |
| 7. #11762722 | C2 | semidirect |
| 9. #11762711 | C2 | semidirect |
| 10. #11762700 | C2 | semidirect |
| 11. C4×C4⋊C4×C17 | C2 | semidirect |
| 57. C42×C17 | D4 | semidirect |
| 147. C4×C4⋊C4 | D17 | semidirect |
| 180. C17 | #2662 | semidirect |
| 214. C42 | D68 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#10587562 | 2 |
| C2×#10587561 | 2 |
| #11762731 | 2 |
| #11762730 | 2 |
| #11762727 | 2 |
| #11762726 | 2 |
| #11762722 | 2 |
| #11762719 | 2 |
| #11762711 | 2 |
| #11762700 | 2 |
| C4×C4⋊C4×C17 | 2 |
| #2662 | 17 |