Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
1176 conjugacy classes of subgroups; only the 347 normal subgroups are shown.
This group has 1176 conjugacy classes of subgroups — too many to draw. Only its 347 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. C33×#135 | C2 | semidirect |
| 2. #11723945 | C2 | semidirect |
| 3. #11722199 | C2 | semidirect |
| 4. #11722198 | C2 | semidirect |
| 5. #11722197 | C2 | semidirect |
| 6. #11722196 | C2 | semidirect |
| 7. C2×C3⋊(C3⋊(C3⋊C16)) | C2 | semidirect |
| 20. C32×#135 | D3 | semidirect |
| 57. C3×#135 | C3⋊D3 | semidirect |
| 99. #135 | C3⋊(C3⋊D3) | semidirect |
| 105. C33 | #508 | semidirect |
| 139. C32 | #5194 | semidirect |
| 162. C3 | #10592893 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C33×#135 | 2 |
| #11723945 | 2 |
| #11722199 | 2 |
| #11722198 | 2 |
| #11722197 | 2 |
| #11722196 | 2 |
| C2×C3⋊(C3⋊(C3⋊C16)) | 2 |
| #10592893 | 3 |