Finite Group DatabasebetaFinite Group DatabasebetaOrder 1296.
282 conjugacy classes of subgroups; only the 60 normal subgroups are shown.
This group has 282 conjugacy classes of subgroups — too many to draw. Only its 60 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. C2×#66364 | C2 | direct (N × H) |
| 6. #66364 | C22 | direct (N × H) |
| 76. C24 | #733 | semidirect |
| 95. C23 | C2×#733 | semidirect |
| 106. C22 | #66364 | direct (N × H) |
| 107. C22 | C22×#733 | semidirect |
| 112. C2 | C2×#66364 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#66364 | 2 |
| C24×3−1+2 | 3 |
| C22×#1094 | 3 |
| C22×C3×C22⋊C9 | 3 |
| C22×#733 | 4 |