Finite Group DatabasebetaFinite Group DatabasebetaOrder 1408.
388 conjugacy classes of subgroups; only the 139 normal subgroups are shown.
This group has 388 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 |
|---|---|---|
| 4. #10622729 | C2 | semidirect |
| 5. C2×#66880 | C2 | semidirect |
| 6. #10622463 | C2 | semidirect |
| 7. #10622462 | C2 | semidirect |
| 8. #10622352 | C2 | semidirect |
| 9. #10622335 | C2 | semidirect |
| 10. C4×Dic44 | C2 | semidirect |
| 11. #10622294 | C2 | semidirect |
| 78. D4×C11 | Q16 | semidirect |
| 198. C11 | #3299 | semidirect |
| 208. D4 | Dic44 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10623074 | 2 |
| D4×Dic22 | 2 |
| C8×D4×C11 | 2 |
| #10622729 | 2 |
| C2×#66880 | 2 |
| #10622463 | 2 |
| #10622462 | 2 |
| #10622352 | 2 |
| #10622335 | 2 |
| C4×Dic44 | 2 |
| #10622294 | 2 |
| #3299 | 11 |