Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
968 conjugacy classes of subgroups; only the 178 normal subgroups are shown.
This group has 968 conjugacy classes of subgroups — too many to draw. Only its 178 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. C2×#88989 | C2 | semidirect |
| 3. C2×C3×#3787 | C2 | semidirect |
| 4. C2×#88926 | C2 | semidirect |
| 5. C2×#88924 | C2 | semidirect |
| 6. #11724252 | C2 | direct (N × H) |
| 16. #88989 | C22 | semidirect |
| 19. C3×#3787 | C22 | semidirect |
| 20. #88926 | C22 | semidirect |
| 21. #88924 | C22 | semidirect |
| 28. C2×#3787 | D3 | semidirect |
| 66. #3787 | C2×D3 | semidirect |
| 114. C2×C33 | #131 | semidirect |
| 168. C33 | C2×#131 | semidirect |
| 203. C2×C32 | #901 | semidirect |
| 248. C32 | C2×#901 | semidirect |
| 269. C2×C3 | #64289 | semidirect |
| 286. C3 | C2×#64289 | semidirect |
| 289. C2 | #11724252 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#89018 | 2 |
| C2×#88989 | 2 |
| C2×C3×#3787 | 2 |
| C2×#88926 | 2 |
| C2×#88924 | 2 |
| #11724252 | 2 |
| C2×#64289 | 3 |
| C2×#901 | 9 |