Finite Group DatabasebetaFinite Group DatabasebetaOrder 2592.
300 conjugacy classes of subgroups; only the 54 normal subgroups are shown.
This group has 300 conjugacy classes of subgroups — too many to draw. Only its 54 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 |
|---|---|---|
| 3. #11722811 | C3 | direct (N × H) |
| 50. C34 | #108 | semidirect |
| 108. C33 | #819 | semidirect |
| 109. C33 | C3×#108 | semidirect |
| 173. C32 | C3×#819 | semidirect |
| 174. C32 | #63748 | semidirect |
| 200. C3 | C3×#63748 | semidirect |
| 201. C3 | #11722811 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#88993 | 2 |
| C2×C32×#622 | 2 |
| #11722811 | 3 |
| C3×#63748 | 3 |
| C3×#819 | 9 |