Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
2092 conjugacy classes of subgroups; only the 452 normal subgroups are shown.
This group has 2092 conjugacy classes of subgroups — too many to draw. Only its 452 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. C22×C32×Dic6 | C2 | semidirect |
| 3. C22×C3⋊(C3⋊(C3⋊C8)) | C2 | semidirect |
| 4. C2×#88793 | C2 | direct (N × H) |
| 13. C2×C32×Dic6 | C22 | semidirect |
| 14. C2×C3⋊(C3⋊(C3⋊C8)) | C22 | semidirect |
| 15. #88793 | C22 | direct (N × H) |
| 19. C22×C3×Dic6 | D3 | semidirect |
| 34. C32×Dic6 | C23 | semidirect |
| 35. C3⋊(C3⋊(C3⋊C8)) | C23 | semidirect |
| 52. C2×C3×Dic6 | C2×D3 | semidirect |
| 58. C22×C33 | SD16 | semidirect |
| 68. C22×Dic6 | C3⋊D3 | semidirect |
| 96. C3×Dic6 | C22×D3 | semidirect |
| 101. C2×C33 | C2×SD16 | semidirect |
| 118. C2×Dic6 | C2×C3⋊D3 | semidirect |
| 126. C22×C32 | #214 | semidirect |
| 127. C22×C32 | #215 | semidirect |
| 146. C33 | C22×SD16 | semidirect |
| 169. Dic6 | C22×C3⋊D3 | semidirect |
| 175. C2×C32 | C2×#214 | semidirect |
| 176. C2×C32 | C2×#215 | semidirect |
| 194. C22×C3 | #3715 | semidirect |
| 195. C22×C3 | #3755 | semidirect |
| 209. C32 | C22×#214 | semidirect |
| 210. C32 | C22×#215 | semidirect |
| 225. C2×C3 | C2×#3715 | semidirect |
| 226. C2×C3 | C2×#3755 | semidirect |
| 232. C22 | #88793 | direct (N × H) |
| 238. C3 | C22×#3715 | semidirect |
| 239. C3 | C22×#3755 | semidirect |
| 241. C2 | C2×#88793 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C3×C4⋊(C3⋊D3) | 2 |
| C22×C32×Dic6 | 2 |
| C22×C3⋊(C3⋊(C3⋊C8)) | 2 |
| C2×#88793 | 2 |
| C22×#3755 | 3 |
| C22×#3715 | 3 |