Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
2943 conjugacy classes of subgroups; only the 555 normal subgroups are shown.
This group has 2943 conjugacy classes of subgroups — too many to draw. Only its 555 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×#88748 | C2 | semidirect |
| 2. C2×Q8×(C3⋊D3)⋊C3 | C2 | semidirect |
| 3. #11722517 | C2 | direct (N × H) |
| 4. C2×#88652 | C2 | semidirect |
| 5. C2×#88651 | C2 | semidirect |
| 6. C2×#88650 | C2 | semidirect |
| 9. #88748 | C22 | semidirect |
| 12. Q8×(C3⋊D3)⋊C3 | C22 | semidirect |
| 19. #88652 | C22 | semidirect |
| 20. #88651 | C22 | semidirect |
| 21. #88650 | C22 | semidirect |
| 22. C2×Q8×C3⋊D3 | D3 | semidirect |
| 49. Q8×C3⋊D3 | C2×D3 | semidirect |
| 119. C2×H(3,𝔽3) | 2−1+4 | semidirect |
| 182. H(3,𝔽3) | C2×2−1+4 | semidirect |
| 224. C2×C32 | #1007 | semidirect |
| 269. C32 | C2×#1007 | semidirect |
| 309. C2 | #11722517 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#88748 | 2 |
| C2×Q8×(C3⋊D3)⋊C3 | 2 |
| #11722517 | 2 |
| C2×#88652 | 2 |
| C2×#88651 | 2 |
| C2×#88650 | 2 |
| C2×#64315 | 3 |