Finite Group DatabasebetaFinite Group DatabasebetaOrder 1408.
404 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 404 conjugacy classes of subgroups — too many to draw. Only its 125 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. #10623098 | C2 | semidirect |
| 3. C4×C11×SD16 | C2 | semidirect |
| 4. #10622788 | C2 | semidirect |
| 5. #10622640 | C2 | semidirect |
| 6. #10622632 | C2 | semidirect |
| 7. #10622465 | C2 | semidirect |
| 8. #10622431 | C2 | semidirect |
| 9. #10622375 | C2 | semidirect |
| 10. #10622306 | C2 | semidirect |
| 11. C8×Dic22 | C2 | semidirect |
| 103. Dic22 | SD16 | semidirect |
| 105. C8×C11 | #41 | semidirect |
| 117. C4×SD16 | D11 | semidirect |
| 205. C11 | #3392 | semidirect |
| 234. C8 | #4339 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10623098 | 2 |
| #10623084 | 2 |
| C4×C11×SD16 | 2 |
| #10622788 | 2 |
| #10622640 | 2 |
| #10622632 | 2 |
| #10622465 | 2 |
| #10622431 | 2 |
| #10622375 | 2 |
| #10622306 | 2 |
| C8×Dic22 | 2 |
| #3392 | 11 |