Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
540 conjugacy classes of subgroups; only the 181 normal subgroups are shown.
This group has 540 conjugacy classes of subgroups — too many to draw. Only its 181 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. #11762713 | C2 | semidirect |
| 3. #11762700 | C2 | semidirect |
| 4. #11762699 | C2 | semidirect |
| 6. #11762680 | C2 | semidirect |
| 7. #11762677 | C2 | semidirect |
| 8. C4×#63227 | C2 | semidirect |
| 9. C4×C4⋊C4×C17 | C2 | semidirect |
| 24. #10587561 | C4 | semidirect |
| 47. C2×Dic34 | C2×C4 | semidirect |
| 51. C42×C17 | C2×C4 | semidirect |
| 55. #63227 | C2×C4 | semidirect |
| 56. #63227 | C2×C4 | semidirect |
| 120. C4×C4⋊C4 | D17 | semidirect |
| 150. C17 | #2337 | semidirect |
| 177. C42 | C4×D17 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#10587561 | 2 |
| #11762713 | 2 |
| #11762700 | 2 |
| #11762699 | 2 |
| #11762687 | 2 |
| #11762680 | 2 |
| #11762677 | 2 |
| C4×#63227 | 2 |
| C4×C4⋊C4×C17 | 2 |
| #2337 | 17 |