Finite Group DatabasebetaFinite Group DatabasebetaOrder 1408.
472 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 472 conjugacy classes of subgroups — too many to draw. Only its 149 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. C22×Dic44 | C2 | semidirect |
| 4. #10622729 | C2 | semidirect |
| 5. #10622462 | C2 | semidirect |
| 6. #10622352 | C2 | semidirect |
| 7. #10622312 | C2 | semidirect |
| 8. C4×Dic44 | C2 | semidirect |
| 54. Dic44 | D4 | direct (N × H) |
| 57. D4×C11 | Q16 | semidirect |
| 86. C22×C11 | C2×Q16 | semidirect |
| 90. C4×C11 | C2×Q16 | semidirect |
| 146. C11 | D4×Q16 | semidirect |
| 153. D4 | Dic44 | direct (N × H) |
| 169. C22 | C2×Dic44 | semidirect |
| 176. C4 | C2×Dic44 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×Dic44 | 2 |
| D4×Dic22 | 2 |
| C8×D4×C11 | 2 |
| #10622729 | 2 |
| #10622462 | 2 |
| #10622352 | 2 |
| #10622312 | 2 |
| C4×Dic44 | 2 |
| D4×Q16 | 11 |