Finite Group DatabasebetaFinite Group DatabasebetaOrder 1408.
362 conjugacy classes of subgroups; only the 115 normal subgroups are shown.
This group has 362 conjugacy classes of subgroups — too many to draw. Only its 115 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. #10623113 | C2 | semidirect |
| 2. C4×C11×Q16 | C2 | semidirect |
| 3. #10622804 | C2 | semidirect |
| 4. #10622801 | C2 | semidirect |
| 5. #10622639 | C2 | semidirect |
| 7. #10622487 | C2 | semidirect |
| 8. #10622425 | C2 | semidirect |
| 9. #10622408 | C2 | semidirect |
| 10. C4×D88 | C2 | semidirect |
| 11. #10622302 | C2 | semidirect |
| 104. C4×Q16 | D11 | semidirect |
| 188. C11 | #3175 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10623113 | 2 |
| C4×C11×Q16 | 2 |
| #10622804 | 2 |
| #10622801 | 2 |
| #10622639 | 2 |
| #10622496 | 2 |
| #10622487 | 2 |
| #10622425 | 2 |
| #10622408 | 2 |
| C4×D88 | 2 |
| #10622302 | 2 |
| #3175 | 11 |