Finite Group DatabasebetaFinite Group DatabasebetaOrder 2304.
474 conjugacy classes of subgroups; only the 102 normal subgroups are shown.
This group has 474 conjugacy classes of subgroups — too many to draw. Only its 102 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. C3×#69085 | C2 | semidirect |
| 3. #11797813 | C2 | semidirect |
| 4. #11773077 | C2 | semidirect |
| 5. #11772984 | C2 | semidirect |
| 6. #11772967 | C2 | semidirect |
| 7. C3×#67519 | C2 | semidirect |
| 21. #10589074 | C4 | semidirect |
| 22. #10589071 | C4 | semidirect |
| 26. #69085 | D3 | semidirect |
| 37. #67519 | D3 | semidirect |
| 51. C3×Dic24 | C2×C4 | semidirect |
| 53. 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 | #10715812 | semidirect |
| 395. C3 | #10715814 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11800601 | 2 |
| C3×#69085 | 2 |
| #11797813 | 2 |
| #11773077 | 2 |
| #11772984 | 2 |
| #11772967 | 2 |
| C3×#67519 | 2 |
| #10715814 | 3 |
| #10715812 | 3 |