Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
371 conjugacy classes of subgroups; only the 112 normal subgroups are shown.
This group has 371 conjugacy classes of subgroups — too many to draw. Only its 112 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. #63431⋊C3 | C2 | semidirect |
| 4. #63366⋊C3 | C2 | semidirect |
| 5. C4⋊(3−1+2⋊C8) | C2 | semidirect |
| 7. #10588690 | C3 | semidirect |
| 24. #63431 | C2×C3 | semidirect |
| 26. #63366 | C2×C3 | semidirect |
| 27. C4⋊(C9⋊C8) | C2×C3 | semidirect |
| 30. D4×3−1+2 | Q8 | semidirect |
| 100. D4×C9 | C3×Q8 | semidirect |
| 171. 3−1+2 | #474 | semidirect |
| 237. C9 | C3×#474 | semidirect |
| 241. D4 | 3−1+2⋊Q8 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×D4×3−1+2 | 2 |
| #63431⋊C3 | 2 |
| #63392⋊C3 | 2 |
| #63366⋊C3 | 2 |
| C4⋊(3−1+2⋊C8) | 2 |
| C3×#5007 | 3 |
| #10588690 | 3 |