Finite Group DatabasebetaFinite Group DatabasebetaOrder 1408.
564 conjugacy classes of subgroups; only the 137 normal subgroups are shown.
This group has 564 conjugacy classes of subgroups — too many to draw. Only its 137 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. C2×#66972 | C2 | semidirect |
| 2. C2×#66969 | C2 | semidirect |
| 3. #10623256 | C2 | semidirect |
| 4. #10623199 | C2 | semidirect |
| 5. C11×#497 | C2 | semidirect |
| 6. #10622803 | C2 | semidirect |
| 7. #10622789 | C2 | semidirect |
| 8. #10622699 | C2 | semidirect |
| 9. #10622671 | C2 | semidirect |
| 10. #10622325 | C2 | semidirect |
| 11. D11×#97 | C2 | semidirect |
| 79. C8×D11 | D4 | semidirect |
| 118. #497 | D11 | semidirect |
| 213. C11 | #3150 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#66972 | 2 |
| C2×#66969 | 2 |
| #10623256 | 2 |
| #10623199 | 2 |
| C11×#497 | 2 |
| #10622803 | 2 |
| #10622789 | 2 |
| #10622699 | 2 |
| #10622671 | 2 |
| #10622325 | 2 |
| D11×#97 | 2 |
| #3150 | 11 |