Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
644 conjugacy classes of subgroups; only the 113 normal subgroups are shown.
This group has 644 conjugacy classes of subgroups — too many to draw. Only its 113 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. C22×C9×D12 | C2 | semidirect |
| 2. C3×#63492 | C2 | semidirect |
| 3. C2×#88421 | C2 | semidirect |
| 4. #11720571 | C2 | semidirect |
| 5. #11720294 | C2 | semidirect |
| 14. C2×C3×D36 | C22 | semidirect |
| 15. C2×C3⋊(C9⋊C8) | C22 | semidirect |
| 17. C3×C4⋊Dic9 | C22 | semidirect |
| 26. #63492 | D3 | semidirect |
| 43. C9×D12 | D4 | semidirect |
| 66. C2×D36 | C2×D3 | semidirect |
| 69. C4⋊Dic9 | C2×D3 | semidirect |
| 74. C22×C3×C9 | D8 | semidirect |
| 87. C22×D12 | D9 | semidirect |
| 189. C22×C9 | #213 | semidirect |
| 204. C3×C9 | #447 | semidirect |
| 238. D12 | #611 | semidirect |
| 284. C22×C3 | #3673 | semidirect |
| 305. C9 | #5036 | semidirect |
| 347. C22 | #88421 | semidirect |
| 353. C3 | #10588898 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C9×D12 | 2 |
| C3×#63492 | 2 |
| C2×#88421 | 2 |
| #11720571 | 2 |
| #11720294 | 2 |
| #10591160 | 3 |
| #10588898 | 3 |