Finite Group DatabasebetaFinite Group DatabasebetaOrder 1296.
251 conjugacy classes of subgroups; only the 58 normal subgroups are shown.
This group has 251 conjugacy classes of subgroups — too many to draw. Only its 58 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. D4×#737 | C2 | semidirect |
| 2. C4⋊#4208 | C2 | semidirect |
| 3. #10619725 | C2 | semidirect |
| 11. C3×D4×C9 | D3 | semidirect |
| 29. #737 | D8 | semidirect |
| 57. C3×C9 | #213 | semidirect |
| 83. D4 | #4208 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D4×#737 | 2 |
| C4⋊#4208 | 2 |
| #10619725 | 2 |
| #88545 | 3 |
| C9×#213 | 3 |