Finite Group DatabasebetaFinite Group DatabasebetaOrder 1944.
698 conjugacy classes of subgroups; only the 112 normal subgroups are shown.
This group has 698 conjugacy classes of subgroups — too many to draw. Only its 112 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 |
|---|---|---|
| 2. C32×C3⋊Dic9 | C2 | semidirect |
| 3. C32×C9×Dic3 | C2 | semidirect |
| 6. #10619872 | C3 | direct (N × H) |
| 9. C3×C3⋊(C3⋊D9) | C4 | semidirect |
| 20. C3×C3⋊Dic9 | D3 | semidirect |
| 21. C3×C3⋊Dic9 | C2×C3 | semidirect |
| 24. C3×C9×Dic3 | D3 | semidirect |
| 25. C3×C9×Dic3 | C2×C3 | semidirect |
| 27. C33×C9 | C2×C4 | semidirect |
| 47. C3⋊(C3⋊D9) | C3×C4 | semidirect |
| 66. C32×Dic3 | D9 | semidirect |
| 79. C3⋊Dic9 | C3×D3 | semidirect |
| 81. C9×Dic3 | C3×D3 | semidirect |
| 93. C32×C9 | C4×D3 | semidirect |
| 94. C32×C9 | C4×D3 | semidirect |
| 95. C32×C9 | C2×C3×C4 | semidirect |
| 167. C3×Dic3 | C3×D9 | semidirect |
| 168. C3×Dic3 | C3⋊D9 | semidirect |
| 182. C33 | C4×D9 | semidirect |
| 199. C3×C9 | #624 | semidirect |
| 200. C3×C9 | C3×C4×D3 | semidirect |
| 201. C3×C9 | C3×C4×D3 | semidirect |
| 261. Dic3 | C3×C3⋊D9 | semidirect |
| 279. C32 | (C3⋊D9)⋊C4 | semidirect |
| 280. C32 | C3×C4×D9 | semidirect |
| 281. C32 | C4×C3⋊D9 | semidirect |
| 288. C9 | C3×#624 | semidirect |
| 317. C3 | C3×(C3⋊D9)⋊C4 | semidirect |
| 318. C3 | #10619872 | direct (N × H) |
| 319. C3 | C3×C4×C3⋊D9 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×C3⋊(C3⋊D9) | 2 |
| C32×C3⋊Dic9 | 2 |
| C32×C9×Dic3 | 2 |
| C3×#6289 | 3 |
| C3×C4×C3⋊D9 | 3 |
| #10619872 | 3 |
| C3×(C3⋊D9)⋊C4 | 3 |