Finite Group DatabasebetaFinite Group DatabasebetaOrder 1296.
224 conjugacy classes of subgroups; only the 58 normal subgroups are shown.
This group has 224 conjugacy classes of subgroups — too many to draw. Only its 58 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 |
|---|---|---|
| 1. D4×#732 | C2 | semidirect |
| 2. #10619650 | C2 | semidirect |
| 3. C2×#66326 | C2 | semidirect |
| 4. C4×#4179 | C2 | semidirect |
| 5. #10619620 | C2 | semidirect |
| 6. #88742 | C3 | semidirect |
| 15. C3×D4×C9 | C2×C3 | semidirect |
| 16. #6233 | C2×C3 | semidirect |
| 17. C2×C3⋊Dic9 | C2×C3 | semidirect |
| 18. C4×C3⋊D9 | C2×C3 | semidirect |
| 19. #6226 | C2×C3 | semidirect |
| 42. #732 | #41 | semidirect |
| 89. C3×C9 | C3×#41 | semidirect |
| 141. D4 | #4179 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D4×#732 | 2 |
| #10619650 | 2 |
| C2×#66326 | 2 |
| C4×#4179 | 2 |
| #10619620 | 2 |
| #88742 | 3 |
| #3830⋊C3 | 3 |