Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
1052 conjugacy classes of subgroups; only the 214 normal subgroups are shown.
This group has 1052 conjugacy classes of subgroups — too many to draw. Only its 214 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×C33×M16 | C2 | semidirect |
| 2. C3×#64139 | C2 | semidirect |
| 3. C2×C3×#3745 | C2 | semidirect |
| 4. C3×#63648 | C2 | semidirect |
| 5. C3×#63644 | C2 | semidirect |
| 6. #10592834 | C3 | direct (N × H) |
| 18. C2×C32×M16 | D3 | semidirect |
| 19. C2×C32×M16 | C2×C3 | semidirect |
| 20. #64139 | C2×C3 | semidirect |
| 21. C2×#3745 | C2×C3 | semidirect |
| 24. #63648 | C2×C3 | semidirect |
| 25. #63644 | C2×C3 | semidirect |
| 39. C33×C8 | D4 | semidirect |
| 76. C2×C3×M16 | C3×D3 | semidirect |
| 77. C2×C3×M16 | C3⋊D3 | semidirect |
| 114. C32×C8 | #67 | semidirect |
| 115. C32×C8 | C3×D4 | semidirect |
| 170. C2×M16 | C3×C3⋊D3 | semidirect |
| 174. C33 | #469 | semidirect |
| 204. C3×C8 | C3×#67 | semidirect |
| 205. C3×C8 | #638 | semidirect |
| 253. C32 | #5135 | semidirect |
| 254. C32 | C3×#469 | semidirect |
| 266. C8 | C3×#638 | semidirect |
| 289. C3 | C3×#5135 | semidirect |
| 290. C3 | #10592834 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C33×M16 | 2 |
| C3×#64139 | 2 |
| C2×C3×#3745 | 2 |
| C3×#63648 | 2 |
| C3×#63644 | 2 |
| #10592834 | 3 |
| C3×#5135 | 3 |