Finite Group DatabasebetaFinite Group DatabasebetaOrder 1408.
388 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 388 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 |
|---|---|---|
| 3. C4×C11×Q16 | C2 | semidirect |
| 4. #10622799 | C2 | semidirect |
| 5. #10622644 | C2 | semidirect |
| 6. #10622634 | C2 | semidirect |
| 7. #10622497 | C2 | semidirect |
| 8. #10622426 | C2 | semidirect |
| 9. D11×#103 | C2 | semidirect |
| 11. #10622294 | C2 | semidirect |
| 92. D44 | Q16 | semidirect |
| 112. C4×Q16 | D11 | semidirect |
| 198. C11 | #3299 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10623110 | 2 |
| Q8×D44 | 2 |
| C4×C11×Q16 | 2 |
| #10622799 | 2 |
| #10622644 | 2 |
| #10622634 | 2 |
| #10622497 | 2 |
| #10622426 | 2 |
| D11×#103 | 2 |
| C8×D44 | 2 |
| #10622294 | 2 |
| #3299 | 11 |