Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
896 conjugacy classes of subgroups; only the 154 normal subgroups are shown.
This group has 896 conjugacy classes of subgroups — too many to draw. Only its 154 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. #11723499 | C2 | semidirect |
| 3. #11723434 | C2 | semidirect |
| 4. C2×#88792 | C2 | semidirect |
| 5. #11722184 | C2 | semidirect |
| 6. C3×#63643 | C2 | semidirect |
| 7. #11722031 | C2 | semidirect |
| 32. #63643 | D3 | semidirect |
| 223. C33 | #463 | semidirect |
| 319. C32 | #4819 | semidirect |
| 320. C32 | #5153 | semidirect |
| 364. C3 | #10590751 | semidirect |
| 365. C3 | #10592852 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C32×D24 | 2 |
| #11723499 | 2 |
| #11723434 | 2 |
| C2×#88792 | 2 |
| #11722184 | 2 |
| C3×#63643 | 2 |
| #11722031 | 2 |
| #10592852 | 3 |
| #10590751 | 3 |