Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
2220 conjugacy classes of subgroups; only the 942 normal subgroups are shown.
This group has 2220 conjugacy classes of subgroups — too many to draw. Only its 942 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. C3×Q8×C3⋊Dic3 | C2 | semidirect |
| 4. #10596283 | C3 | direct (N × H) |
| 6. C2×C33×Q8 | C4 | semidirect |
| 15. Q8×C3⋊Dic3 | C2×C3 | semidirect |
| 28. C2×C32×Q8 | Dic3 | semidirect |
| 29. C2×C32×Q8 | C3×C4 | semidirect |
| 73. C2×C3×Q8 | C3×Dic3 | semidirect |
| 74. C2×C3×Q8 | C3⋊Dic3 | semidirect |
| 103. C33 | #519 | semidirect |
| 127. C2×Q8 | C3×C3⋊Dic3 | semidirect |
| 148. C32 | #5812 | semidirect |
| 149. C32 | C3×#519 | semidirect |
| 170. C3 | C3×#5812 | semidirect |
| 171. C3 | #10596283 | 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 |
| C3×Q8×C3⋊Dic3 | 2 |
| C3×#64135 | 2 |
| #10596283 | 3 |
| C3×#5812 | 3 |