Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
864 conjugacy classes of subgroups; only the 222 normal subgroups are shown.
This group has 864 conjugacy classes of subgroups — too many to draw. Only its 222 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. C3×C9×#127 | C2 | semidirect |
| 2. C3×#63501 | C2 | semidirect |
| 3. C3×#63499 | C2 | semidirect |
| 4. C3×#63497 | C2 | semidirect |
| 5. C3×#63438 | C2 | semidirect |
| 7. #10589822 | C3 | direct (N × H) |
| 10. C2×C3×D4×C9 | C22 | semidirect |
| 12. C22×C3×Dic9 | C22 | semidirect |
| 13. C3×C42×C9 | C22 | semidirect |
| 15. C3×#3676 | C22 | semidirect |
| 17. C3×Dic9⋊C4 | C22 | semidirect |
| 24. C9×#127 | C2×C3 | semidirect |
| 25. #63501 | C2×C3 | semidirect |
| 26. #63499 | C2×C3 | semidirect |
| 27. #63497 | C2×C3 | semidirect |
| 28. #63438 | C2×C3 | semidirect |
| 55. C2×D4×C9 | C22×C3 | semidirect |
| 57. C22×Dic9 | C22×C3 | semidirect |
| 59. C42×C9 | C22×C3 | semidirect |
| 61. #3676 | C22×C3 | semidirect |
| 63. Dic9⋊C4 | C22×C3 | semidirect |
| 73. C3×#127 | D9 | semidirect |
| 119. C2×C3×D4 | C2×D9 | semidirect |
| 130. C3×C42 | C2×D9 | semidirect |
| 157. #127 | C3×D9 | semidirect |
| 162. C3×C9 | #560 | semidirect |
| 202. C2×D4 | C2×C3×D9 | semidirect |
| 208. C42 | C2×C3×D9 | semidirect |
| 232. C9 | C3×#560 | semidirect |
| 263. C3 | #10589822 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×C9×#127 | 2 |
| C3×#63501 | 2 |
| C3×#63499 | 2 |
| C3×#63497 | 2 |
| C3×#63438 | 2 |
| C3×#5720 | 3 |
| #10589822 | 3 |