Finite Group DatabasebetaFinite Group DatabasebetaOrder 7776.
578 conjugacy classes of subgroups; only the 54 normal subgroups are shown.
This group has 578 conjugacy classes of subgroups — too many to draw. Only its 54 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. #72229362 | C2 | semidirect |
| 2. C2×#11757417⋊C2 | C2 | semidirect |
| 4. C22×#11757417 | C2 | semidirect |
| 23. #11757417 | D4 | semidirect |
| 27. #11720654 | C9 | semidirect |
| 61. C22×C22⋊C27 | C2×C9 | semidirect |
| 62. C2×(C22⋊C27)⋊C2 | C2×C9 | semidirect |
| 69. (C22⋊C27)⋊C4 | C2×C9 | semidirect |
| 210. C22⋊C27 | D4×C9 | semidirect |
| 427. C24 | AGL(1,ℤ/27) | semidirect |
| 514. C22 | #14516071 | semidirect |
| 515. C22 | #11757417⋊C2 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #72229362 | 2 |
| C2×#11757417⋊C2 | 2 |
| #72229306 | 3 |
| C22×#11757417 | 2 |
| #72220060 | 3 |
| #14516071 | 4 |