Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
354 conjugacy classes of subgroups; only the 83 normal subgroups are shown.
This group has 354 conjugacy classes of subgroups — too many to draw. Only its 83 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. #11720906 | C2 | semidirect |
| 3. #11720541 | C2 | semidirect |
| 4. C9×(C2×D3)⋊C8 | C2 | semidirect |
| 5. C3×#63380 | C2 | semidirect |
| 6. #11720283 | C2 | semidirect |
| 7. #11720278 | C2 | semidirect |
| 32. #63380 | D3 | semidirect |
| 99. (C2×D3)⋊C8 | D9 | semidirect |
| 206. C3×C9 | #482 | semidirect |
| 296. C9 | #4784 | semidirect |
| 338. C3 | #10588419 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11721037 | 2 |
| #11720906 | 2 |
| #11720541 | 2 |
| C9×(C2×D3)⋊C8 | 2 |
| C3×#63380 | 2 |
| #11720283 | 2 |
| #11720278 | 2 |
| #10590834 | 3 |
| #10588419 | 3 |