Finite Group DatabasebetaFinite Group DatabasebetaOrder 2304.
612 conjugacy classes of subgroups; only the 171 normal subgroups are shown.
This group has 612 conjugacy classes of subgroups — too many to draw. Only its 171 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. #11797595 | C2 | semidirect |
| 3. #11772190 | C2 | semidirect |
| 4. #11771658 | C2 | semidirect |
| 5. #11771655 | C2 | semidirect |
| 6. #11771325 | C2 | semidirect |
| 7. C32×#2171 | C2 | semidirect |
| 24. C3×#2171 | D3 | semidirect |
| 43. #63656 | C8 | semidirect |
| 44. #63655 | C8 | semidirect |
| 45. #63654 | C8 | semidirect |
| 46. #63653 | C8 | semidirect |
| 98. #2171 | C3⋊D3 | semidirect |
| 270. C32 | #12068 | semidirect |
| 300. C3 | #10707075 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11797868 | 2 |
| #11797595 | 2 |
| #11772190 | 2 |
| #11771658 | 2 |
| #11771655 | 2 |
| #11771325 | 2 |
| C32×#2171 | 2 |
| #10707075 | 3 |