Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
1067 conjugacy classes of subgroups; only the 179 normal subgroups are shown.
This group has 1067 conjugacy classes of subgroups — too many to draw. Only its 179 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. C22×#634⋊C3 | C2 | semidirect |
| 3. C2×#3748⋊C3 | C2 | semidirect |
| 4. C2×#88439 | C2 | semidirect |
| 5. C2×#88437 | C2 | semidirect |
| 6. #11721069 | C2 | direct (N × H) |
| 20. C2×#634⋊C3 | C22 | semidirect |
| 21. #3748⋊C3 | C22 | semidirect |
| 23. #88439 | C22 | semidirect |
| 24. #88437 | C22 | semidirect |
| 25. C22×#634 | D3 | semidirect |
| 30. C2×#3748 | D3 | semidirect |
| 67. C2×#634 | C2×D3 | semidirect |
| 91. #3748 | C2×D3 | semidirect |
| 181. C2×H(3,𝔽3) | #137 | semidirect |
| 274. H(3,𝔽3) | C2×#137 | semidirect |
| 350. C2×C32 | #909 | semidirect |
| 351. C2×C32 | #942 | semidirect |
| 413. C32 | C2×#909 | semidirect |
| 414. C32 | C2×#942 | semidirect |
| 466. C2 | #11721069 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#88740 | 2 |
| C22×#634⋊C3 | 2 |
| C2×#3748⋊C3 | 2 |
| C2×#88439 | 2 |
| C2×#88437 | 2 |
| #11721069 | 2 |
| C2×#63831 | 3 |
| C2×#63827 | 3 |