Finite Group DatabasebetaFinite Group DatabasebetaOrder 2304.
582 conjugacy classes of subgroups; only the 131 normal subgroups are shown.
This group has 582 conjugacy classes of subgroups — too many to draw. Only its 131 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. #11797874 | C2 | semidirect |
| 3. #11797807 | C2 | semidirect |
| 4. #11773068 | C2 | semidirect |
| 5. #11772980 | C2 | semidirect |
| 6. #11772672 | C2 | semidirect |
| 7. C32×#1418 | C2 | semidirect |
| 16. #10589387 | C4 | semidirect |
| 17. #10589385 | C4 | semidirect |
| 25. C3×#1418 | D3 | semidirect |
| 33. C32×Q32 | C2×C4 | semidirect |
| 35. C32×D16 | C2×C4 | semidirect |
| 46. C3⋊(C3⋊C32) | C2×C4 | semidirect |
| 85. #1418 | C3⋊D3 | semidirect |
| 91. C3×Q32 | C4×D3 | semidirect |
| 93. C3×D16 | C4×D3 | semidirect |
| 166. Q32 | C4×C3⋊D3 | semidirect |
| 170. D16 | C4×C3⋊D3 | semidirect |
| 228. C32 | #13658 | semidirect |
| 258. C3 | #10715809 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11800584 | 2 |
| #11797874 | 2 |
| #11797807 | 2 |
| #11773068 | 2 |
| #11772980 | 2 |
| #11772672 | 2 |
| C32×#1418 | 2 |
| #10715809 | 3 |