Finite Group DatabasebetaFinite Group DatabasebetaOrder 1408.
362 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 362 conjugacy classes of subgroups — too many to draw. Only its 117 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. #10623116 | C2 | semidirect |
| 2. #10623074 | C2 | semidirect |
| 3. C4×C11×SD16 | C2 | semidirect |
| 4. #10622778 | C2 | semidirect |
| 5. #10622634 | C2 | semidirect |
| 7. #10622484 | C2 | semidirect |
| 8. #10622413 | C2 | semidirect |
| 9. #10622369 | C2 | semidirect |
| 10. #10622307 | C2 | semidirect |
| 11. C8×Dic22 | C2 | semidirect |
| 110. C4×SD16 | D11 | semidirect |
| 195. C11 | #3361 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10623116 | 2 |
| #10623074 | 2 |
| C4×C11×SD16 | 2 |
| #10622778 | 2 |
| #10622634 | 2 |
| #10622628 | 2 |
| #10622484 | 2 |
| #10622413 | 2 |
| #10622369 | 2 |
| #10622307 | 2 |
| C8×Dic22 | 2 |
| #3361 | 11 |