Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
2828 conjugacy classes of subgroups; only the 1075 normal subgroups are shown.
This group has 2828 conjugacy classes of subgroups — too many to draw. Only its 1075 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×C4⋊(C3⋊(C3⋊Dic3)) | C2 | semidirect |
| 3. C22×C3⋊(C3⋊(C3⋊C8)) | C2 | semidirect |
| 4. #11722202 | C2 | direct (N × H) |
| 9. C2×C33×D4 | C4 | semidirect |
| 14. C4⋊(C3⋊(C3⋊Dic3)) | C22 | semidirect |
| 16. C2×C3⋊(C3⋊(C3⋊C8)) | C22 | semidirect |
| 28. C33×D4 | C2×C4 | semidirect |
| 40. C2×C32×D4 | Dic3 | semidirect |
| 71. C32×D4 | C2×Dic3 | semidirect |
| 81. C2×C33 | #102 | semidirect |
| 88. C2×C3×D4 | C3⋊Dic3 | semidirect |
| 112. C33 | C2×#102 | semidirect |
| 120. C3×D4 | C2×C3⋊Dic3 | semidirect |
| 129. C2×C32 | #832 | semidirect |
| 136. C2×D4 | C3⋊(C3⋊Dic3) | semidirect |
| 156. C32 | C2×#832 | semidirect |
| 164. D4 | C2×C3⋊(C3⋊Dic3) | semidirect |
| 173. C2×C3 | #63659 | semidirect |
| 189. C3 | C2×#63659 | semidirect |
| 191. C2 | #11722202 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C33×D4 | 2 |
| C2×C4⋊(C3⋊(C3⋊Dic3)) | 2 |
| C22×C3⋊(C3⋊(C3⋊C8)) | 2 |
| #11722202 | 2 |
| C2×#63659 | 3 |