Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
359 conjugacy classes of subgroups; only the 112 normal subgroups are shown.
This group has 359 conjugacy classes of subgroups — too many to draw. Only its 112 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 |
|---|---|---|
| 7. #10588707 | C3 | semidirect |
| 71. C4×3−1+2 | Q16 | semidirect |
| 157. C4×C9 | C3×Q16 | semidirect |
| 166. 3−1+2 | #462 | semidirect |
| 226. C9 | C3×#462 | semidirect |
| 249. C4 | #3674⋊C3 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×Q8×3−1+2 | 2 |
| C2×#3674⋊C3 | 2 |
| #63431⋊C3 | 2 |
| #63368⋊C3 | 2 |
| C4⋊(3−1+2⋊C8) | 2 |
| C3×#5031 | 3 |
| #10588707 | 3 |