Finite Group DatabasebetaFinite Group DatabasebetaOrder 704.
120 conjugacy classes of subgroups; only the 39 normal subgroups are shown.
This group has 120 conjugacy classes of subgroups — too many to draw. Only its 39 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. #66999 | C2 | semidirect |
| 2. C2×#4325 | C2 | semidirect |
| 3. C2×#4313 | C2 | semidirect |
| 5. C11×#103 | C2 | semidirect |
| 6. #66885 | C2 | semidirect |
| 7. #66871 | C2 | semidirect |
| 36. C11⋊C8 | D4 | semidirect |
| 56. #103 | D11 | semidirect |
| 76. C11 | #468 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #66999 | 2 |
| C2×#4325 | 2 |
| C2×#4313 | 2 |
| #66948 | 2 |
| C11×#103 | 2 |
| #66885 | 2 |
| #66871 | 2 |
| #468 | 11 |