Finite Group DatabasebetaFinite Group DatabasebetaOrder 2304.
270 conjugacy classes of subgroups; only the 86 normal subgroups are shown.
This group has 270 conjugacy classes of subgroups — too many to draw. Only its 86 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. C3×#67519 | C2 | semidirect |
| 3. C32×#1368 | C2 | semidirect |
| 4. #10682654 | C3 | direct (N × H) |
| 17. C3×#1368 | D3 | semidirect |
| 18. C3×#1368 | C2×C3 | semidirect |
| 19. #67519 | C2×C3 | semidirect |
| 28. C3×Dic24 | C8 | semidirect |
| 30. C3×D48 | C8 | semidirect |
| 65. #1368 | C3×D3 | semidirect |
| 89. Dic24 | C3×C8 | semidirect |
| 91. D48 | C3×C8 | semidirect |
| 226. C32 | #7389 | semidirect |
| 253. C3 | C3×#7389 | semidirect |
| 254. C3 | #10682654 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#69085 | 2 |
| C3×#67519 | 2 |
| C32×#1368 | 2 |
| #10682654 | 3 |
| C3×#7389 | 3 |