Finite Group DatabasebetaFinite Group DatabasebetaOrder 2304.
582 conjugacy classes of subgroups; only the 171 normal subgroups are shown.
This group has 582 conjugacy classes of subgroups — too many to draw. Only its 171 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 |
|---|---|---|
| 1. #11797874 | C2 | semidirect |
| 2. #11797810 | C2 | semidirect |
| 3. #11773071 | C2 | semidirect |
| 4. #11772977 | C2 | semidirect |
| 5. #11772960 | C2 | semidirect |
| 6. #11772672 | C2 | semidirect |
| 13. C32×SD64 | C4 | semidirect |
| 14. C32×D32 | C4 | semidirect |
| 33. C32×Q32 | C2×C4 | semidirect |
| 37. C32×D16 | C2×C4 | semidirect |
| 45. C32×C32 | C2×C4 | semidirect |
| 52. C3×SD64 | Dic3 | semidirect |
| 53. C3×D32 | Dic3 | semidirect |
| 91. C3×Q32 | C2×Dic3 | semidirect |
| 95. C3×D16 | C2×Dic3 | semidirect |
| 103. C3×C32 | C2×Dic3 | semidirect |
| 124. SD64 | C3⋊Dic3 | semidirect |
| 125. D32 | C3⋊Dic3 | semidirect |
| 166. Q32 | C2×C3⋊Dic3 | semidirect |
| 170. D16 | C2×C3⋊Dic3 | semidirect |
| 179. C32 | C2×C3⋊Dic3 | semidirect |
| 228. C32 | #13658 | semidirect |
| 258. C3 | #10715813 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11797874 | 2 |
| #11797810 | 2 |
| #11773071 | 2 |
| #11772977 | 2 |
| #11772960 | 2 |
| #11772672 | 2 |
| C32×#2263 | 2 |
| #10715813 | 3 |