Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
1836 conjugacy classes of subgroups; only the 338 normal subgroups are shown.
This group has 1836 conjugacy classes of subgroups — too many to draw. Only its 338 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 |
|---|---|---|
| 1. C22×C33×Q8 | C2 | semidirect |
| 3. C3×#63658 | C2 | semidirect |
| 4. #10592930 | C3 | direct (N × H) |
| 12. C22×C32×Q8 | D3 | semidirect |
| 13. C22×C32×Q8 | C2×C3 | semidirect |
| 16. #63658 | C2×C3 | semidirect |
| 21. C22×C3×C3⋊D3 | Q8 | semidirect |
| 50. C22×C3×Q8 | C3×D3 | semidirect |
| 51. C22×C3×Q8 | C3⋊D3 | semidirect |
| 61. C22×C3⋊D3 | C3×Q8 | semidirect |
| 115. C22×Q8 | C3×C3⋊D3 | semidirect |
| 118. C33 | #393 | semidirect |
| 178. C32 | #5231 | semidirect |
| 179. C32 | C3×#393 | semidirect |
| 209. C3 | C3×#5231 | semidirect |
| 210. C3 | #10592930 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C33×Q8 | 2 |
| C2×C3×#3752 | 2 |
| C3×#63658 | 2 |
| #10592930 | 3 |
| C3×#5231 | 3 |