Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
371 conjugacy classes of subgroups; only the 56 normal subgroups are shown.
This group has 371 conjugacy classes of subgroups — too many to draw. Only its 56 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. C22×C3×Q8⋊C9 | C2 | semidirect |
| 2. C2×C3×#3689 | C2 | semidirect |
| 3. C3×#63421 | C2 | semidirect |
| 5. #10589523 | C3 | direct (N × H) |
| 15. C22×Q8⋊C9 | C2×C3 | semidirect |
| 16. C2×#3689 | C2×C3 | semidirect |
| 20. #63421 | C2×C3 | semidirect |
| 25. C3×Q8⋊C9 | D4 | semidirect |
| 57. C22×C3×Q8 | D9 | semidirect |
| 93. Q8⋊C9 | C3×D4 | semidirect |
| 156. C22×Q8 | C3×D9 | semidirect |
| 179. C3×Q8 | #611 | semidirect |
| 244. C22×C3 | #3689 | semidirect |
| 270. Q8 | C3×#611 | semidirect |
| 300. C22 | C3×#3689 | semidirect |
| 307. C3 | #10589523 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C3×Q8⋊C9 | 2 |
| C2×C3×#3689 | 2 |
| C3×#63421 | 2 |
| C3×#5227 | 3 |
| #10589523 | 3 |
| C2×C3×#611 | 4 |