Finite Group DatabasebetaFinite Group DatabasebetaOrder 864.
300 conjugacy classes of subgroups; only the 76 normal subgroups are shown.
This group has 300 conjugacy classes of subgroups — too many to draw. Only its 76 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. #88448 | C2 | semidirect |
| 5. #88447 | C2 | semidirect |
| 10. C2×(C3⋊Dic3)⋊C3 | C4 | semidirect |
| 38. C2×C3⋊Dic3 | Dic3 | semidirect |
| 87. H(3,𝔽3) | #117 | semidirect |
| 148. C32 | #877 | semidirect |
| 149. C32 | #926 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×(C3⋊Dic3)⋊C3 | 2 |
| #88552 | 2 |
| #3757⋊C3 | 2 |
| #88448 | 2 |
| #88447 | 2 |
| #63957 | 3 |
| #63955 | 3 |