Finite Group DatabasebetaFinite Group DatabasebetaOrder 1944.
262 conjugacy classes of subgroups; only the 35 normal subgroups are shown.
This group has 262 conjugacy classes of subgroups — too many to draw. Only its 35 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. #11757832 | C2 | semidirect |
| 3. C3⋊D3×C22⋊C9 | C3 | semidirect |
| 5. (C3⋊D3)⋊(C22⋊C9) | C3 | semidirect |
| 11. C3×#1094 | D3 | semidirect |
| 12. C32×C22⋊C9 | C2×C3 | semidirect |
| 15. C32⋊(C22⋊C9) | C2×C3 | semidirect |
| 59. C22×C3⋊D3 | 3−1+2 | semidirect |
| 91. C22×C32 | C2×3−1+2 | semidirect |
| 105. C22⋊C9 | (C3⋊D3)⋊C3 | semidirect |
| 139. C3⋊D3 | #1094 | semidirect |
| 172. C32 | C2×#1094 | semidirect |
| 197. C22 | #92262 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11757832 | 2 |
| C22×C3×(C3⋊D3)⋊C3 | 3 |
| C3⋊D3×C22⋊C9 | 3 |
| D3×#1094 | 3 |
| (C3⋊D3)⋊(C22⋊C9) | 3 |
| #92262 | 4 |