Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
2140 conjugacy classes of subgroups; only the 307 normal subgroups are shown.
This group has 2140 conjugacy classes of subgroups — too many to draw. Only its 307 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×D4×C3⋊D9 | C2 | semidirect |
| 2. C3×C9×#127 | C2 | semidirect |
| 3. #11721838 | C2 | semidirect |
| 4. #11721837 | C2 | semidirect |
| 5. C4×C4⋊(C3⋊D9) | C2 | semidirect |
| 8. C23×C3⋊D9 | C22 | semidirect |
| 9. C2×C3×D4×C9 | C22 | semidirect |
| 10. C2×C3×D4×C9 | C22 | semidirect |
| 11. C2×#6233 | C22 | semidirect |
| 14. C2×C4×C3⋊D9 | C22 | semidirect |
| 15. C3×C42×C9 | C22 | semidirect |
| 16. #88551 | C22 | semidirect |
| 17. #88536 | C22 | semidirect |
| 18. C4⋊(C3⋊Dic9) | C22 | semidirect |
| 25. C9×#127 | D3 | semidirect |
| 39. C4⋊(C3⋊D9) | D4 | semidirect |
| 55. C2×D4×C9 | C2×D3 | semidirect |
| 56. C2×D4×C9 | C2×D3 | semidirect |
| 61. C42×C9 | C2×D3 | semidirect |
| 71. C2×C3⋊D9 | C2×D4 | semidirect |
| 73. C3×C4×C9 | C2×D4 | semidirect |
| 77. C3×#127 | D9 | semidirect |
| 116. C2×C3×D4 | C2×D9 | semidirect |
| 117. C2×C3×D4 | C2×D9 | semidirect |
| 128. C3×C42 | C2×D9 | semidirect |
| 154. C4×C9 | D3×D4 | semidirect |
| 157. #127 | C3⋊D9 | semidirect |
| 161. C3×C9 | D42 | semidirect |
| 198. C2×D4 | C2×C3⋊D9 | semidirect |
| 199. C2×D4 | C2×C3⋊D9 | semidirect |
| 204. C42 | C2×C3⋊D9 | semidirect |
| 221. C3×C4 | D4×D9 | semidirect |
| 226. C9 | #5717 | semidirect |
| 256. C4 | D4×C3⋊D9 | semidirect |
| 257. C3 | #10589819 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×D4×C3⋊D9 | 2 |
| C3×C9×#127 | 2 |
| #11721838 | 2 |
| #11721837 | 2 |
| C4×C4⋊(C3⋊D9) | 2 |
| #10596188 | 3 |
| #10589819 | 3 |