Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
296 conjugacy classes of subgroups; only the 65 normal subgroups are shown.
This group has 296 conjugacy classes of subgroups — too many to draw. Only its 65 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. C9×#919 | C2 | semidirect |
| 2. D3×D72 | C2 | semidirect |
| 3. #11720567 | C2 | semidirect |
| 4. C3×#63387 | C2 | semidirect |
| 5. #11720239 | C2 | semidirect |
| 6. #11720238 | C2 | semidirect |
| 7. #11720237 | C2 | semidirect |
| 12. C3×C9×Q16 | C22 | semidirect |
| 15. C9×D24 | C22 | semidirect |
| 19. C3⋊(C9⋊C16) | C22 | semidirect |
| 20. C3×C9⋊C16 | C22 | semidirect |
| 32. #63387 | D3 | semidirect |
| 63. C9×Q16 | C2×D3 | semidirect |
| 73. C9⋊C16 | C2×D3 | semidirect |
| 83. #919 | D9 | semidirect |
| 133. C3×Q16 | C2×D9 | semidirect |
| 146. D24 | C2×D9 | semidirect |
| 179. C3×C9 | #509 | semidirect |
| 219. Q16 | D3×D9 | semidirect |
| 249. C9 | #4914 | semidirect |
| 282. C3 | #10588873 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C9×#919 | 2 |
| D3×D72 | 2 |
| #11720567 | 2 |
| C3×#63387 | 2 |
| #11720239 | 2 |
| #11720238 | 2 |
| #11720237 | 2 |
| #10591038 | 3 |
| #10588873 | 3 |