Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
670 conjugacy classes of subgroups; only the 101 normal subgroups are shown.
This group has 670 conjugacy classes of subgroups — too many to draw. Only its 101 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×C3×D4×D9 | C2 | semidirect |
| 2. C2×#88544 | C2 | semidirect |
| 3. #11721004 | C2 | semidirect |
| 4. C2×#88417 | C2 | semidirect |
| 5. C9×#832 | C2 | semidirect |
| 6. (C2×D9)⋊(C3⋊C8) | C2 | semidirect |
| 7. #11720266 | C2 | semidirect |
| 12. C2×C4⋊(C3⋊D9) | C22 | semidirect |
| 20. C2×C3⋊(C9⋊C8) | C22 | semidirect |
| 21. C9×C4⋊Dic3 | C22 | semidirect |
| 22. C2×C9×C3⋊C8 | C22 | semidirect |
| 29. C2×D4×D9 | D3 | semidirect |
| 48. C3×D4×C9 | D4 | semidirect |
| 56. C3×D36 | D4 | semidirect |
| 111. C2×C3×D9 | D8 | semidirect |
| 127. #832 | D9 | semidirect |
| 165. D4×C9 | #67 | semidirect |
| 177. D36 | #67 | semidirect |
| 219. C4⋊Dic3 | C2×D9 | semidirect |
| 223. C2×C3⋊C8 | C2×D9 | semidirect |
| 263. C2×D9 | #213 | semidirect |
| 277. C3×C9 | #447 | semidirect |
| 301. C3×D4 | D36 | semidirect |
| 411. C9 | #5217 | semidirect |
| 426. D4 | #6192 | semidirect |
| 472. C3 | #10588453 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×D4×D9 | 2 |
| C2×#88544 | 2 |
| #11721004 | 2 |
| C2×#88417 | 2 |
| C9×#832 | 2 |
| (C2×D9)⋊(C3⋊C8) | 2 |
| #11720266 | 2 |
| #10591448 | 3 |
| #10588453 | 3 |