Finite Group DatabasebetaFinite Group DatabasebetaOrder 2304.
636 conjugacy classes of subgroups; only the 145 normal subgroups are shown.
This group has 636 conjugacy classes of subgroups — too many to draw. Only its 145 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. #11797624 | C2 | semidirect |
| 3. #11772908 | C2 | semidirect |
| 4. #11772658 | C2 | semidirect |
| 5. C32×#1424 | C2 | semidirect |
| 14. #10589314 | C4 | semidirect |
| 17. C3×#1424 | D3 | semidirect |
| 28. #63626 | C2×C4 | semidirect |
| 29. C32×C32 | C2×C4 | semidirect |
| 54. #1424 | C3⋊D3 | semidirect |
| 66. C3×C32 | C4×D3 | semidirect |
| 116. C32 | C4×C3⋊D3 | semidirect |
| 150. C32 | #13654 | semidirect |
| 172. C3 | #10715789 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#10589314 | 2 |
| #11797624 | 2 |
| #11772908 | 2 |
| #11772658 | 2 |
| C32×#1424 | 2 |
| #10715789 | 3 |