Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
3612 conjugacy classes of subgroups; only the 1115 normal subgroups are shown.
This group has 3612 conjugacy classes of subgroups — too many to draw. Only its 1115 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 |
|---|---|---|
| 3. C2×#88853 | C2 | direct (N × H) |
| 10. #88853 | C22 | direct (N × H) |
| 28. C22×C33 | Q16 | semidirect |
| 44. C2×C33 | C2×Q16 | semidirect |
| 52. C22×C32 | Dic12 | semidirect |
| 60. C33 | C22×Q16 | semidirect |
| 68. C2×C32 | C2×Dic12 | semidirect |
| 76. C22×C3 | #3746 | semidirect |
| 81. C32 | C22×Dic12 | semidirect |
| 89. C2×C3 | C2×#3746 | semidirect |
| 91. C22 | #88853 | direct (N × H) |
| 96. C3 | C22×#3746 | semidirect |
| 97. C2 | C2×#88853 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#6308 | 2 |
| C22×C33×C8 | 2 |
| C2×#88853 | 2 |
| C22×#3746 | 3 |