Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
1428 conjugacy classes of subgroups; only the 405 normal subgroups are shown.
This group has 1428 conjugacy classes of subgroups — too many to draw. Only its 405 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. #11723931 | C2 | semidirect |
| 5. #11722187 | C2 | semidirect |
| 6. #11722184 | C2 | semidirect |
| 7. #11722177 | C2 | semidirect |
| 115. C33 | #478 | semidirect |
| 154. C32 | #4763 | semidirect |
| 182. C3 | #10592462 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D4×C3⋊(C3⋊Dic3) | 2 |
| #11723931 | 2 |
| C33×#102 | 2 |
| #11722202 | 2 |
| #11722187 | 2 |
| #11722184 | 2 |
| #11722177 | 2 |
| #10592462 | 3 |