Finite Group DatabasebetaFinite Group DatabasebetaOrder 2304.
474 conjugacy classes of subgroups; only the 100 normal subgroups are shown.
This group has 474 conjugacy classes of subgroups — too many to draw. Only its 100 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. #11797893 | C2 | semidirect |
| 3. #11797810 | C2 | semidirect |
| 4. #11773077 | C2 | semidirect |
| 5. C3×#67825 | C2 | semidirect |
| 6. #11772967 | C2 | semidirect |
| 7. #11772681 | C2 | semidirect |
| 17. C3×#4520 | C4 | semidirect |
| 18. C3×#4519 | C4 | semidirect |
| 32. #67825 | D3 | semidirect |
| 50. C3×Dic24 | C2×C4 | semidirect |
| 52. C3×D48 | C2×C4 | semidirect |
| 55. C3×C3⋊C32 | C2×C4 | semidirect |
| 76. #4520 | Dic3 | semidirect |
| 77. #4519 | Dic3 | semidirect |
| 152. Dic24 | C2×Dic3 | semidirect |
| 154. D48 | C2×Dic3 | semidirect |
| 158. C3⋊C32 | C2×Dic3 | semidirect |
| 356. C32 | #13658 | semidirect |
| 394. C3 | #10715813 | semidirect |
| 395. C3 | #10715815 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#71458 | 2 |
| #11797893 | 2 |
| #11797810 | 2 |
| #11773077 | 2 |
| C3×#67825 | 2 |
| #11772967 | 2 |
| #11772681 | 2 |
| #10715815 | 3 |
| #10715813 | 3 |