Finite Group DatabasebetaFinite Group DatabasebetaOrder 2304.
342 conjugacy classes of subgroups; only the 78 normal subgroups are shown.
This group has 342 conjugacy classes of subgroups — too many to draw. Only its 78 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. C3×#67514 | C2 | semidirect |
| 18. #67519 | D3 | semidirect |
| 19. #67514 | D3 | semidirect |
| 242. C32 | #7390 | semidirect |
| 271. C3 | #10682657 | semidirect |
| 272. C3 | #10682659 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11797813 | 2 |
| C3×#67519 | 2 |
| C3×#67514 | 2 |
| #10682659 | 3 |
| #10682657 | 3 |