Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
884 conjugacy classes of subgroups; only the 188 normal subgroups are shown.
This group has 884 conjugacy classes of subgroups — too many to draw. Only its 188 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. C2×C3×C4⋊(C3⋊Dic3) | C2 | semidirect |
| 3. #11722200 | C2 | semidirect |
| 4. #11722056 | C2 | semidirect |
| 5. #11722031 | C2 | semidirect |
| 18. C2×C4⋊(C3⋊Dic3) | D3 | semidirect |
| 169. C33 | #480 | semidirect |
| 249. C32 | #4967 | semidirect |
| 250. C32 | #5033 | semidirect |
| 288. C3 | #10591089 | semidirect |
| 289. C3 | #10592732 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×C4⋊(C3⋊Dic3) | 2 |
| C32×#930 | 2 |
| #11722200 | 2 |
| #11722056 | 2 |
| #11722031 | 2 |
| #10592732 | 3 |
| #10591089 | 3 |