Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
1848 conjugacy classes of subgroups; only the 629 normal subgroups are shown.
This group has 1848 conjugacy classes of subgroups — too many to draw. Only its 629 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. D4×C3⋊(C3⋊Dic3) | C2 | semidirect |
| 3. #11722202 | C2 | semidirect |
| 4. #11722187 | C2 | semidirect |
| 5. #11722185 | C2 | semidirect |
| 9. C33×D8 | C4 | semidirect |
| 22. C33×D4 | C2×C4 | semidirect |
| 27. C33×C8 | C2×C4 | semidirect |
| 32. C32×D8 | Dic3 | semidirect |
| 53. C32×D4 | C2×Dic3 | semidirect |
| 58. C32×C8 | C2×Dic3 | semidirect |
| 66. C3×D8 | C3⋊Dic3 | semidirect |
| 85. C33 | #442 | semidirect |
| 88. C3×D4 | C2×C3⋊Dic3 | semidirect |
| 93. C3×C8 | C2×C3⋊Dic3 | semidirect |
| 100. D8 | C3⋊(C3⋊Dic3) | semidirect |
| 114. C32 | #5152 | semidirect |
| 117. D4 | C2×C3⋊(C3⋊Dic3) | semidirect |
| 123. C8 | C2×C3⋊(C3⋊Dic3) | semidirect |
| 135. C3 | #10592851 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C33×D8 | 2 |
| D4×C3⋊(C3⋊Dic3) | 2 |
| #11722202 | 2 |
| #11722187 | 2 |
| #11722185 | 2 |
| #10592851 | 3 |