Finite Group DatabasebetaFinite Group DatabasebetaOrder 1408.
472 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 472 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. C2×#66971 | C2 | semidirect |
| 3. Q8×D44 | C2 | semidirect |
| 4. C11×#462 | C2 | semidirect |
| 5. #10622799 | C2 | semidirect |
| 6. #10622705 | C2 | semidirect |
| 7. C4×#4325 | C2 | semidirect |
| 8. #10622454 | C2 | semidirect |
| 9. #10622451 | C2 | semidirect |
| 10. #10622429 | C2 | semidirect |
| 11. #10622423 | C2 | semidirect |
| 67. #4325 | D4 | semidirect |
| 118. #462 | D11 | semidirect |
| 135. C4×C11 | #137 | semidirect |
| 216. C11 | #3276 | semidirect |
| 261. C4 | #66971 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#66971 | 2 |
| #10623257 | 2 |
| Q8×D44 | 2 |
| C11×#462 | 2 |
| #10622799 | 2 |
| #10622705 | 2 |
| C4×#4325 | 2 |
| #10622454 | 2 |
| #10622451 | 2 |
| #10622429 | 2 |
| #10622423 | 2 |
| #3276 | 11 |