Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
2212 conjugacy classes of subgroups; only the 463 normal subgroups are shown.
This group has 2212 conjugacy classes of subgroups — too many to draw. Only its 463 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. C22×#6308 | C2 | semidirect |
| 3. C2×#88861 | C2 | semidirect |
| 4. #11722200 | C2 | semidirect |
| 5. #11722180 | C2 | semidirect |
| 35. #6308 | D4 | semidirect |
| 54. C22×C33 | SD16 | semidirect |
| 101. C22×C32 | #214 | semidirect |
| 112. C33 | #448 | semidirect |
| 148. C22×C3 | #3754 | semidirect |
| 154. C32 | #5040 | semidirect |
| 179. C22 | #88861 | semidirect |
| 185. C3 | #10592739 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#6308 | 2 |
| C33×#121 | 2 |
| C2×#88861 | 2 |
| #11722200 | 2 |
| #11722180 | 2 |
| #10592739 | 3 |