Finite Group DatabasebetaFinite Group DatabasebetaOrder 1408.
472 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 472 conjugacy classes of subgroups — too many to draw. Only its 133 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×Q16×D11 | C2 | semidirect |
| 4. C11×#462 | C2 | semidirect |
| 5. #10622799 | C2 | semidirect |
| 6. #10622705 | C2 | semidirect |
| 7. C4×#4326 | C2 | semidirect |
| 8. #10622462 | C2 | semidirect |
| 10. #10622426 | C2 | semidirect |
| 11. #10622421 | C2 | semidirect |
| 66. #4326 | D4 | semidirect |
| 98. D44 | Q16 | semidirect |
| 118. #462 | D11 | semidirect |
| 126. C2×D11 | C2×Q16 | semidirect |
| 131. C4×C11 | C2×Q16 | semidirect |
| 212. C11 | D4×Q16 | semidirect |
| 254. C4 | Q16×D11 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×Q16×D11 | 2 |
| #10623258 | 2 |
| Q8×D44 | 2 |
| C11×#462 | 2 |
| #10622799 | 2 |
| #10622705 | 2 |
| C4×#4326 | 2 |
| #10622462 | 2 |
| #10622447 | 2 |
| #10622426 | 2 |
| #10622421 | 2 |
| D4×Q16 | 11 |