Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
898 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 898 conjugacy classes of subgroups — too many to draw. Only its 107 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×Q8×C22⋊C9 | C2 | semidirect |
| 2. C4⋊(C3⋊((C22⋊C9)⋊C2)) | C2 | semidirect |
| 3. C4×C3⋊((C22⋊C9)⋊C2) | C2 | semidirect |
| 17. Q8×C22⋊C9 | D3 | semidirect |
| 46. C3×C22⋊C9 | #41 | semidirect |
| 49. C22×C3×Q8 | D9 | semidirect |
| 127. C22⋊C9 | #239 | semidirect |
| 131. C22×Q8 | C3⋊D9 | semidirect |
| 146. C3×Q8 | (C22⋊C9)⋊C2 | semidirect |
| 194. C22×C3 | #3701 | semidirect |
| 218. Q8 | C3⋊((C22⋊C9)⋊C2) | semidirect |
| 243. C22 | #88746 | semidirect |
| 249. C3 | #10593094 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×Q8×C22⋊C9 | 2 |
| C4⋊(C3⋊((C22⋊C9)⋊C2)) | 2 |
| C4×C3⋊((C22⋊C9)⋊C2) | 2 |
| #10596288 | 3 |
| #10593094 | 3 |
| #88746 | 4 |