Finite Group DatabasebetaFinite Group DatabasebetaOrder 1408.
738 conjugacy classes of subgroups; only the 157 normal subgroups are shown.
This group has 738 conjugacy classes of subgroups — too many to draw. Only its 157 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. C23×Dic22 | C2 | semidirect |
| 3. C2×#67004 | C2 | semidirect |
| 4. #10622820 | C2 | semidirect |
| 5. #10622663 | C2 | semidirect |
| 6. #10622653 | C2 | semidirect |
| 7. #10622617 | C2 | semidirect |
| 23. C2×#4326 | C22 | semidirect |
| 24. C2×#4324 | C22 | semidirect |
| 27. #66874 | C22 | semidirect |
| 49. C2×Dic22 | D4 | semidirect |
| 103. C22×C11 | #137 | semidirect |
| 169. C11 | #3004 | semidirect |
| 204. C22 | #67004 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×Dic22 | 2 |
| C11×#525 | 2 |
| C2×#67004 | 2 |
| #10622820 | 2 |
| #10622663 | 2 |
| #10622653 | 2 |
| #10622617 | 2 |
| #3004 | 11 |