Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
2268 conjugacy classes of subgroups; only the 407 normal subgroups are shown.
This group has 2268 conjugacy classes of subgroups — too many to draw. Only its 407 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. C2×#89078 | C2 | semidirect |
| 2. C2×C33×D8 | C2 | semidirect |
| 3. #11723979 | C2 | semidirect |
| 4. C2×#88861 | C2 | semidirect |
| 5. #11722202 | C2 | semidirect |
| 6. #11722190 | C2 | semidirect |
| 7. #11722186 | C2 | semidirect |
| 25. C2×C32×D8 | D3 | semidirect |
| 37. C33×D4 | D4 | semidirect |
| 48. #6308 | D4 | semidirect |
| 83. C2×C3×D8 | C3⋊D3 | semidirect |
| 95. C32×D4 | #67 | semidirect |
| 148. C2×D8 | C3⋊(C3⋊D3) | semidirect |
| 153. C33 | #449 | semidirect |
| 160. C3×D4 | #638 | semidirect |
| 210. C32 | #5158 | semidirect |
| 221. D4 | #6312 | semidirect |
| 252. C3 | #10592857 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#89078 | 2 |
| C2×C33×D8 | 2 |
| #11723979 | 2 |
| C2×#88861 | 2 |
| #11722202 | 2 |
| #11722190 | 2 |
| #11722186 | 2 |
| #10592857 | 3 |