Finite Group DatabasebetaFinite Group DatabasebetaOrder 1408.
584 conjugacy classes of subgroups; only the 173 normal subgroups are shown.
This group has 584 conjugacy classes of subgroups — too many to draw. Only its 173 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×#4314 | C2 | semidirect |
| 3. C2×C4×Dic22 | C2 | semidirect |
| 4. C2×C11×C4⋊C8 | C2 | semidirect |
| 5. C2×#66885 | C2 | semidirect |
| 6. #10622461 | C2 | direct (N × H) |
| 17. C2×#4314 | C22 | semidirect |
| 21. C4×Dic22 | C22 | semidirect |
| 22. C11×C4⋊C8 | C22 | semidirect |
| 23. #66885 | C22 | semidirect |
| 40. C2×Dic22 | D4 | semidirect |
| 58. C2×C4×C11 | SD16 | semidirect |
| 76. Dic22 | C2×D4 | semidirect |
| 82. C2×C4⋊C8 | D11 | semidirect |
| 94. C4×C11 | C2×SD16 | semidirect |
| 114. C4⋊C8 | C2×D11 | semidirect |
| 116. C2×C11 | #460 | semidirect |
| 148. C11 | C2×#460 | semidirect |
| 167. C2×C4 | #4314 | semidirect |
| 187. C4 | C2×#4314 | semidirect |
| 191. C2 | #10622461 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#4314 | 2 |
| C2×#66927 | 2 |
| C2×C4×Dic22 | 2 |
| C2×C11×C4⋊C8 | 2 |
| C2×#66885 | 2 |
| #10622461 | 2 |
| C2×#460 | 11 |