Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
940 conjugacy classes of subgroups; only the 175 normal subgroups are shown.
This group has 940 conjugacy classes of subgroups — too many to draw. Only its 175 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. C3×C9×C22⋊Q8 | C2 | semidirect |
| 3. C2×#88548 | C2 | semidirect |
| 4. #11720571 | C2 | semidirect |
| 5. #11720528 | C2 | semidirect |
| 9. C2×C3×Q8×C9 | C22 | semidirect |
| 15. C3×C9×C4⋊C4 | C22 | semidirect |
| 18. C2×C3⋊(C9⋊C8) | C22 | semidirect |
| 25. C9×C22⋊Q8 | D3 | semidirect |
| 58. C2×Q8×C9 | C2×D3 | semidirect |
| 64. C9×C4⋊C4 | C2×D3 | semidirect |
| 70. C22×C3×C9 | SD16 | semidirect |
| 82. C3×C22⋊Q8 | D9 | semidirect |
| 128. C2×C3×Q8 | C2×D9 | semidirect |
| 140. C3×C4⋊C4 | C2×D9 | semidirect |
| 162. C22×C9 | #215 | semidirect |
| 174. C22⋊Q8 | C3⋊D9 | semidirect |
| 177. C3×C9 | #450 | semidirect |
| 219. C2×Q8 | C2×C3⋊D9 | semidirect |
| 227. C4⋊C4 | C2×C3⋊D9 | semidirect |
| 233. C22×C3 | #3675 | semidirect |
| 254. C9 | #5046 | semidirect |
| 286. C22 | #88548 | semidirect |
| 292. C3 | #10588729 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C4⋊(C3⋊D9) | 2 |
| C3×C9×C22⋊Q8 | 2 |
| C2×#88548 | 2 |
| #11720571 | 2 |
| #11720528 | 2 |
| #10592745 | 3 |
| #10588729 | 3 |