Finite Group DatabasebetaFinite Group Databasebeta← C2×C3⋊((C22⋊C9)⋊C8) #13147035
Order 1728.
490 conjugacy classes of subgroups; only the 131 normal subgroups are shown.
This group has 490 conjugacy classes of subgroups — too many to draw. Only its 131 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. C3⋊((C22⋊C9)⋊C8) | C2 | direct (N × H) |
| 16. C2×C3×C22⋊C9 | C8 | semidirect |
| 40. C3×C22⋊C9 | C2×C8 | semidirect |
| 67. C2×C22⋊C9 | C3⋊C8 | semidirect |
| 116. C22⋊C9 | C2×C3⋊C8 | semidirect |
| 131. C23×C3 | C9⋊C8 | semidirect |
| 191. C22×C3 | C2×C9⋊C8 | semidirect |
| 208. C23 | C3⋊(C9⋊C8) | semidirect |
| 227. C2×C3 | (C22⋊C9)⋊C8 | semidirect |
| 238. C22 | C2×C3⋊(C9⋊C8) | semidirect |
| 244. C3 | C2×(C22⋊C9)⋊C8 | semidirect |
| 249. C2 | C3⋊((C22⋊C9)⋊C8) | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×C4×C22⋊C9 | 2 |
| C3⋊((C22⋊C9)⋊C8) | 2 |
| C2×#63657 | 3 |
| C2×(C22⋊C9)⋊C8 | 3 |
| C2×C3⋊(C9⋊C8) | 4 |