Finite Group DatabasebetaFinite Group DatabasebetaOrder 1408.
352 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 352 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. #10623115 | C2 | semidirect |
| 3. C4×C11×SD16 | C2 | semidirect |
| 4. #10622784 | C2 | semidirect |
| 5. #10622634 | C2 | semidirect |
| 6. #10622620 | C2 | semidirect |
| 7. #10622473 | C2 | semidirect |
| 8. #10622428 | C2 | semidirect |
| 9. #10622392 | C2 | semidirect |
| 10. C8×D44 | C2 | semidirect |
| 11. #10622293 | C2 | semidirect |
| 107. C4×SD16 | D11 | semidirect |
| 193. C11 | #3340 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10623115 | 2 |
| #10623094 | 2 |
| C4×C11×SD16 | 2 |
| #10622784 | 2 |
| #10622634 | 2 |
| #10622620 | 2 |
| #10622473 | 2 |
| #10622428 | 2 |
| #10622392 | 2 |
| C8×D44 | 2 |
| #10622293 | 2 |
| #3340 | 11 |