Finite Group DatabasebetaFinite Group DatabasebetaOrder 2304.
762 conjugacy classes of subgroups; only the 187 normal subgroups are shown.
This group has 762 conjugacy classes of subgroups — too many to draw. Only its 187 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. #11777137 | C2 | semidirect |
| 3. #11771564 | C2 | semidirect |
| 4. #11771294 | C2 | semidirect |
| 5. C32×#1372 | C2 | semidirect |
| 19. C3×#1372 | D3 | semidirect |
| 35. #63626 | C8 | semidirect |
| 58. #3745 | C2×C8 | semidirect |
| 61. C32×C16 | C2×C8 | semidirect |
| 65. #1372 | C3⋊D3 | semidirect |
| 121. C3×C16 | D3×C8 | semidirect |
| 180. C16 | C8×C3⋊D3 | semidirect |
| 190. C32 | #12045 | semidirect |
| 219. C3 | #10706937 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×#63626 | 2 |
| #11777137 | 2 |
| #11771564 | 2 |
| #11771294 | 2 |
| C32×#1372 | 2 |
| #10706937 | 3 |