Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
840 conjugacy classes of subgroups; only the 144 normal subgroups are shown.
This group has 840 conjugacy classes of subgroups — too many to draw. Only its 144 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 |
|---|---|---|
| 4. C2×#88799 | C2 | semidirect |
| 5. #11722060 | C2 | semidirect |
| 6. #11722030 | C2 | semidirect |
| 7. #11722028 | C2 | semidirect |
| 222. C33 | #473 | semidirect |
| 309. C32 | #5143 | semidirect |
| 310. C32 | #5204 | semidirect |
| 344. C3 | #10591682 | semidirect |
| 345. C3 | #10592903 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11723992 | 2 |
| C3×#64157 | 2 |
| C32×#951 | 2 |
| C2×#88799 | 2 |
| #11722060 | 2 |
| #11722030 | 2 |
| #11722028 | 2 |
| #10592903 | 3 |
| #10591682 | 3 |