Finite Group DatabasebetaFinite Group DatabasebetaOrder 1944.
223 conjugacy classes of subgroups; only the 34 normal subgroups are shown.
This group has 223 conjugacy classes of subgroups — too many to draw. Only its 34 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. #11757857 | C2 | semidirect |
| 2. C9×C3⋊S4 | C3 | semidirect |
| 5. (C3⋊S4)⋊C9 | C3 | semidirect |
| 7. C22×C3×3−1+2 | D3 | semidirect |
| 11. C3×C9×A4 | C2×C3 | semidirect |
| 15. (C3×A4)⋊C9 | C2×C3 | semidirect |
| 53. C3×3−1+2 | S4 | semidirect |
| 59. C3⋊S4 | 3−1+2 | semidirect |
| 93. C3×A4 | C2×3−1+2 | semidirect |
| 101. C22×C9 | (C3⋊D3)⋊C3 | semidirect |
| 169. C9 | (C3⋊S4)⋊C3 | semidirect |
| 181. C22 | #92262 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11757857 | 2 |
| C9×C3⋊S4 | 3 |
| C3×(C3⋊S4)⋊C3 | 3 |
| #67×3−1+2 | 3 |
| (C3⋊S4)⋊C9 | 3 |
| #92262 | 4 |