Finite Group DatabasebetaFinite Group DatabasebetaOrder 1408.
356 conjugacy classes of subgroups; only the 139 normal subgroups are shown.
This group has 356 conjugacy classes of subgroups — too many to draw. Only its 139 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. #10622704 | C2 | semidirect |
| 4. #10622691 | C2 | semidirect |
| 5. #10622664 | C2 | semidirect |
| 6. #10622657 | C2 | semidirect |
| 7. C4×#4326 | C2 | semidirect |
| 8. #10622634 | C2 | semidirect |
| 10. #10622583 | C2 | semidirect |
| 11. C2×#66871 | C2 | semidirect |
| 78. D4×C11 | Q16 | semidirect |
| 190. C11 | #3338 | semidirect |
| 198. D4 | #4326 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C11×#554 | 2 |
| #10623074 | 2 |
| #10622704 | 2 |
| #10622691 | 2 |
| #10622664 | 2 |
| #10622657 | 2 |
| C4×#4326 | 2 |
| #10622634 | 2 |
| D4×C11⋊C8 | 2 |
| #10622583 | 2 |
| C2×#66871 | 2 |
| #3338 | 11 |