Finite Group DatabasebetaFinite Group DatabasebetaOrder 1408.
376 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 376 conjugacy classes of subgroups — too many to draw. Only its 133 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. #10623050 | C2 | semidirect |
| 3. C11×#428 | C2 | semidirect |
| 5. #10622732 | C2 | semidirect |
| 7. C2×#66871 | C2 | semidirect |
| 8. #10622503 | C2 | semidirect |
| 9. #10622488 | C2 | semidirect |
| 10. #10622484 | C2 | semidirect |
| 11. #10622470 | C2 | semidirect |
| 46. #4339 | Q8 | semidirect |
| 108. #428 | D11 | semidirect |
| 198. C11 | #3083 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10623050 | 2 |
| #10623035 | 2 |
| C11×#428 | 2 |
| #10622746 | 2 |
| #10622732 | 2 |
| #10622615 | 2 |
| C2×#66871 | 2 |
| #10622503 | 2 |
| #10622488 | 2 |
| #10622484 | 2 |
| #10622470 | 2 |
| #3083 | 11 |