Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
910 conjugacy classes of subgroups; only the 222 normal subgroups are shown.
This group has 910 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×#120 | C2 | semidirect |
| 2. C3×#63515 | C2 | semidirect |
| 3. C3×#63499 | C2 | semidirect |
| 4. C3×#63498 | C2 | semidirect |
| 5. C3×#63447 | C2 | semidirect |
| 7. #10589696 | C3 | direct (N × H) |
| 8. C24×C3×C9 | C22 | semidirect |
| 9. C23×C3×D9 | C22 | semidirect |
| 12. C2×C3×Dic18 | C22 | semidirect |
| 13. C3×C9×C22⋊C4 | C22 | semidirect |
| 14. C3×#3676 | C22 | semidirect |
| 15. C3×#3676 | C22 | semidirect |
| 16. C3×(C2×D9)⋊C4 | C22 | semidirect |
| 17. C3×C4×Dic9 | C22 | semidirect |
| 24. C9×#120 | C2×C3 | semidirect |
| 25. #63515 | C2×C3 | semidirect |
| 26. #63499 | C2×C3 | semidirect |
| 27. #63498 | C2×C3 | semidirect |
| 28. #63447 | C2×C3 | semidirect |
| 47. C24×C9 | C22×C3 | semidirect |
| 48. C23×D9 | C22×C3 | semidirect |
| 57. C2×Dic18 | C22×C3 | semidirect |
| 59. C9×C22⋊C4 | C22×C3 | semidirect |
| 60. #3676 | C22×C3 | semidirect |
| 61. #3676 | C22×C3 | semidirect |
| 62. (C2×D9)⋊C4 | C22×C3 | semidirect |
| 63. C4×Dic9 | C22×C3 | semidirect |
| 78. C3×#120 | D9 | semidirect |
| 116. C24×C3 | C2×D9 | semidirect |
| 130. C3×C22⋊C4 | C2×D9 | semidirect |
| 165. #120 | C3×D9 | semidirect |
| 166. C3×C9 | H(3,𝔽4) | semidirect |
| 204. C24 | C2×C3×D9 | semidirect |
| 211. C22⋊C4 | C2×C3×D9 | semidirect |
| 239. C9 | C3×H(3,𝔽4) | semidirect |
| 271. C3 | #10589696 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×C9×#120 | 2 |
| C3×#63515 | 2 |
| C3×#63499 | 2 |
| C3×#63498 | 2 |
| C3×#63447 | 2 |
| C3×#5594 | 3 |
| #10589696 | 3 |