Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
296 conjugacy classes of subgroups; only the 77 normal subgroups are shown.
This group has 296 conjugacy classes of subgroups — too many to draw. Only its 77 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×C9×D24 | C2 | semidirect |
| 2. C3×#63467 | C2 | semidirect |
| 3. #11720534 | C2 | semidirect |
| 4. #11720240 | C2 | semidirect |
| 5. #11720238 | C2 | semidirect |
| 13. C3×D72 | C22 | semidirect |
| 15. C3×Dic36 | C22 | semidirect |
| 16. C3⋊(C9⋊C16) | C22 | semidirect |
| 23. #63467 | D3 | semidirect |
| 55. D72 | C2×D3 | semidirect |
| 57. Dic36 | C2×D3 | semidirect |
| 70. C2×D24 | D9 | semidirect |
| 148. C3×C9 | #509 | semidirect |
| 210. C9 | #5193 | semidirect |
| 239. C3 | #10588827 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C9×D24 | 2 |
| C3×#63467 | 2 |
| #11720534 | 2 |
| #11720240 | 2 |
| #11720238 | 2 |
| #10590630 | 3 |
| #10588827 | 3 |