Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
1284 conjugacy classes of subgroups; only the 220 normal subgroups are shown.
This group has 1284 conjugacy classes of subgroups — too many to draw. Only its 220 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 |
|---|---|---|
| 2. C32×#869 | C2 | semidirect |
| 3. C2×#88795 | C2 | semidirect |
| 4. C3×C4×C3⋊(C3⋊C8) | C2 | semidirect |
| 19. C3×#869 | D3 | semidirect |
| 21. C4×C3⋊(C3⋊C8) | D3 | semidirect |
| 30. C3×C3⋊(C3⋊C8) | D4 | semidirect |
| 53. C33×C4 | SD16 | semidirect |
| 62. #869 | C3⋊D3 | semidirect |
| 84. C3⋊(C3⋊C8) | D12 | semidirect |
| 119. C32×C4 | #204 | semidirect |
| 120. C32×C4 | #215 | semidirect |
| 128. C33 | #492 | semidirect |
| 178. C3×C4 | #3717 | semidirect |
| 179. C3×C4 | #3755 | semidirect |
| 184. C32 | #4693 | semidirect |
| 185. C32 | #5085 | semidirect |
| 207. C4 | #88795 | semidirect |
| 210. C3 | #10590373 | semidirect |
| 211. C3 | #10592784 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11723915 | 2 |
| C32×#869 | 2 |
| C2×#88795 | 2 |
| C3×C4×C3⋊(C3⋊C8) | 2 |
| #10592784 | 3 |
| #10590373 | 3 |