Finite Group DatabasebetaFinite Group DatabasebetaOrder 1296.
332 conjugacy classes of subgroups; only the 82 normal subgroups are shown.
This group has 332 conjugacy classes of subgroups — too many to draw. Only its 82 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C2 | C22×#4169 |
| commutator, cosocle | C2×C3×C9 | C23×C3 |
| Frattini, socle | C2×C32 | C22×C3×D3 |
| Fitting | D4×C32⋊C9 | C2 |
| hypercenter | D4 | #4169 |
| hypocenter | C3×C9 | C3×#41 |
| LCS | G ▷ C2×C3×C9 ▷ C3×C9 | |
| UCS | C1 ◁ C2 ◁ D4 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. D4×C32⋊C9 | C2 | semidirect |
| 2. #10619630 | C2 | semidirect |
| 3. C2×#66316 | C2 | semidirect |
| 4. C4×#4169 | C2 | semidirect |
| 5. #10619590 | C2 | semidirect |
| 7. #88742 | C3 | semidirect |
| 19. C3×D4×C9 | C2×C3 | semidirect |
| 20. #6233 | C2×C3 | semidirect |
| 21. C2×C3⋊Dic9 | C2×C3 | semidirect |
| 22. C4×C3⋊D9 | C2×C3 | semidirect |
| 23. #6226 | C2×C3 | semidirect |
| 44. C32⋊C9 | #41 | semidirect |
| 48. C32×D4 | D9 | semidirect |
| 115. C3×C9 | C3×#41 | semidirect |
| 182. C32 | #3699 | semidirect |
| 188. D4 | #4169 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D4×C32⋊C9 | 2 |
| #10619630 | 2 |
| C2×#66316 | 2 |
| C4×#4169 | 2 |
| #10619590 | 2 |
| C3×#3830 | 3 |
| #88742 | 3 |