Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
488 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 488 conjugacy classes of subgroups — too many to draw. Only its 125 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 |
|---|---|---|
| 4. #11723092 | C2 | direct (N × H) |
| 8. C2×C3⋊#622 | C4 | semidirect |
| 11. #88988 | C4 | semidirect |
| 13. C2×C33×C8 | C4 | semidirect |
| 14. C2×C3×C3⋊(C3⋊C8) | C4 | semidirect |
| 15. C3×C8×C3⋊D3 | C4 | semidirect |
| 31. C3⋊#622 | C2×C4 | semidirect |
| 32. C33×C8 | C2×C4 | semidirect |
| 33. C3×C3⋊(C3⋊C8) | C2×C4 | semidirect |
| 45. C2×C32×C8 | Dic3 | semidirect |
| 46. C2×C3⋊(C3⋊C8) | Dic3 | semidirect |
| 47. C8×C3⋊D3 | Dic3 | semidirect |
| 86. C32×C8 | C2×Dic3 | semidirect |
| 87. C3⋊(C3⋊C8) | C2×Dic3 | semidirect |
| 90. C2×C33 | #97 | semidirect |
| 92. C3×C3⋊D3 | #97 | semidirect |
| 102. C2×C3×C8 | #157 | semidirect |
| 135. C33 | C2×#97 | semidirect |
| 156. C3×C8 | C2×#157 | semidirect |
| 163. C2×C32 | #815 | semidirect |
| 165. C3⋊D3 | #815 | semidirect |
| 177. C2×C8 | C3⋊#157 | semidirect |
| 202. C32 | C2×#815 | semidirect |
| 214. C8 | C2×C3⋊#157 | semidirect |
| 221. C2×C3 | #63767 | semidirect |
| 236. C3 | C2×#63767 | semidirect |
| 239. C2 | #11723092 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C4×C3⋊#157 | 2 |
| C2×#88988 | 2 |
| C2×C3×C8×C3⋊D3 | 2 |
| #11723092 | 2 |
| C2×#63767 | 3 |
| C2×#815 | 9 |