Finite Group DatabasebetaFinite Group DatabasebetaOrder 2304.
216 conjugacy classes of subgroups; only the 110 normal subgroups are shown.
This group has 216 conjugacy classes of subgroups — too many to draw. Only its 110 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 |
|---|---|---|
| 4. #10682523 | C3 | direct (N × H) |
| 24. C3×C3⋊C32 | C8 | semidirect |
| 67. C3⋊C32 | C3×C8 | semidirect |
| 150. C32 | #7333 | semidirect |
| 168. C3 | C3×#7333 | semidirect |
| 169. C3 | #10682523 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#67519 | 2 |
| C32×#1313 | 2 |
| #10682523 | 3 |
| C3×#7333 | 3 |