Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
1284 conjugacy classes of subgroups; only the 236 normal subgroups are shown.
This group has 1284 conjugacy classes of subgroups — too many to draw. Only its 236 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. C3×#64078 | C2 | semidirect |
| 3. C2×#88797 | C2 | semidirect |
| 4. C32×C4×C3⋊C8 | C2 | semidirect |
| 18. #64078 | D3 | semidirect |
| 22. C3×C4×C3⋊C8 | D3 | semidirect |
| 30. C32×C3⋊C8 | D4 | semidirect |
| 53. C33×C4 | SD16 | semidirect |
| 64. C4×C3⋊C8 | C3⋊D3 | semidirect |
| 85. C3×C3⋊C8 | D12 | semidirect |
| 118. C32×C4 | #204 | semidirect |
| 119. C32×C4 | #215 | semidirect |
| 128. C33 | #492 | semidirect |
| 149. C3⋊C8 | C4⋊(C3⋊D3) | semidirect |
| 178. C3×C4 | #3717 | semidirect |
| 179. C3×C4 | #3744 | semidirect |
| 184. C32 | #4693 | semidirect |
| 185. C32 | #5085 | semidirect |
| 207. C4 | #88797 | semidirect |
| 210. C3 | #10590373 | semidirect |
| 211. C3 | #10592392 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11723915 | 2 |
| C3×#64078 | 2 |
| C2×#88797 | 2 |
| C32×C4×C3⋊C8 | 2 |
| #10592392 | 3 |
| #10590373 | 3 |