Finite Group DatabasebetaFinite Group DatabasebetaOrder 1408.
352 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 352 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. #10623073 | C2 | semidirect |
| 3. C8×D4×C11 | C2 | semidirect |
| 4. #10622727 | C2 | semidirect |
| 5. #10622719 | C2 | semidirect |
| 6. #10622463 | C2 | semidirect |
| 7. #10622459 | C2 | semidirect |
| 8. #10622350 | C2 | semidirect |
| 9. #10622336 | C2 | semidirect |
| 10. C4×#4314 | C2 | semidirect |
| 11. #10622293 | C2 | semidirect |
| 108. C8×D4 | D11 | semidirect |
| 193. C11 | #3340 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10623094 | 2 |
| #10623073 | 2 |
| C8×D4×C11 | 2 |
| #10622727 | 2 |
| #10622719 | 2 |
| #10622463 | 2 |
| #10622459 | 2 |
| #10622350 | 2 |
| #10622336 | 2 |
| C4×#4314 | 2 |
| #10622293 | 2 |
| #3340 | 11 |