Finite Group DatabasebetaFinite Group DatabasebetaOrder 1408.
420 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 420 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 |
|---|---|---|
| 2. Q8×D44 | C2 | semidirect |
| 3. C11×#475 | C2 | semidirect |
| 4. #10622706 | C2 | semidirect |
| 5. C4×#4325 | C2 | semidirect |
| 6. #10622477 | C2 | semidirect |
| 7. #10622475 | C2 | semidirect |
| 8. #10622454 | C2 | semidirect |
| 9. #10622447 | C2 | semidirect |
| 10. #10622419 | C2 | semidirect |
| 11. D11×#103 | C2 | semidirect |
| 82. Q8×C11 | #41 | semidirect |
| 95. D44 | SD16 | semidirect |
| 111. #475 | D11 | semidirect |
| 205. C11 | #3298 | semidirect |
| 213. Q8 | #4343 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10623257 | 2 |
| Q8×D44 | 2 |
| C11×#475 | 2 |
| #10622706 | 2 |
| C4×#4325 | 2 |
| #10622477 | 2 |
| #10622475 | 2 |
| #10622454 | 2 |
| #10622447 | 2 |
| #10622419 | 2 |
| D11×#103 | 2 |
| #3298 | 11 |