Finite Group DatabasebetaFinite Group DatabasebetaOrder 2304.
474 conjugacy classes of subgroups; only the 90 normal subgroups are shown.
This group has 474 conjugacy classes of subgroups — too many to draw. Only its 90 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. #11797893 | C2 | semidirect |
| 3. #11797807 | C2 | semidirect |
| 4. C3×#67579 | C2 | semidirect |
| 5. #11772984 | C2 | semidirect |
| 6. C3×#67580 | C2 | semidirect |
| 7. #11772681 | C2 | semidirect |
| 21. #10589074 | C4 | semidirect |
| 22. #10589071 | C4 | semidirect |
| 36. #67580 | D3 | semidirect |
| 37. #67579 | D3 | semidirect |
| 50. C3×Dic24 | C2×C4 | semidirect |
| 52. C3×D48 | C2×C4 | semidirect |
| 55. C3×C3⋊C32 | C2×C4 | semidirect |
| 146. Dic24 | C4×D3 | semidirect |
| 154. D48 | C4×D3 | semidirect |
| 158. C3⋊C32 | C4×D3 | semidirect |
| 356. C32 | #13658 | semidirect |
| 394. C3 | #10715809 | semidirect |
| 395. C3 | #10715811 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11800601 | 2 |
| #11797893 | 2 |
| #11797807 | 2 |
| C3×#67579 | 2 |
| #11772984 | 2 |
| C3×#67580 | 2 |
| #11772681 | 2 |
| #10715811 | 3 |
| #10715809 | 3 |