Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
7084 conjugacy classes of subgroups; only the 1523 normal subgroups are shown.
This group has 7084 conjugacy classes of subgroups — too many to draw. Only its 1523 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×#88864 | C2 | semidirect |
| 5. C24×C33 | C4 | semidirect |
| 7. C22×C3⋊(C3⋊Dic3) | C22 | semidirect |
| 20. C24×C32 | Dic3 | semidirect |
| 27. C22×C33 | C22⋊C4 | semidirect |
| 45. C24×C3 | C3⋊Dic3 | semidirect |
| 52. C22×C32 | #217 | semidirect |
| 58. C33 | #379 | semidirect |
| 70. C24 | C3⋊(C3⋊Dic3) | semidirect |
| 77. C22×C3 | #3757 | semidirect |
| 81. C32 | #5247 | semidirect |
| 95. C22 | #88864 | semidirect |
| 99. C3 | #10592946 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C25×C33 | 2 |
| C2×#88864 | 2 |
| #10592946 | 3 |