Finite Group DatabasebetaFinite Group DatabasebetaOrder 1408.
572 conjugacy classes of subgroups; only the 153 normal subgroups are shown.
This group has 572 conjugacy classes of subgroups — too many to draw. Only its 153 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. C2×C11×#135 | C2 | semidirect |
| 2. #10623363 | C2 | semidirect |
| 3. C2×#67003 | C2 | semidirect |
| 4. C2×#66957 | C2 | semidirect |
| 5. #10622804 | C2 | semidirect |
| 6. #10622794 | C2 | semidirect |
| 7. #10622788 | C2 | semidirect |
| 8. #10622781 | C2 | semidirect |
| 9. #10622768 | C2 | semidirect |
| 10. #10622764 | C2 | semidirect |
| 11. C2×C8×Dic11 | C2 | semidirect |
| 58. C2×C8×C11 | D4 | semidirect |
| 71. C2×C11⋊C8 | D4 | semidirect |
| 109. C2×#135 | D11 | semidirect |
| 131. Dic11 | #135 | semidirect |
| 193. C2×C8 | C22⋊D11 | semidirect |
| 202. C11 | #3147 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C11×#135 | 2 |
| #10623363 | 2 |
| C2×#67003 | 2 |
| C2×#66957 | 2 |
| #10622804 | 2 |
| #10622794 | 2 |
| #10622788 | 2 |
| #10622781 | 2 |
| #10622768 | 2 |
| #10622764 | 2 |
| C2×C8×Dic11 | 2 |
| #3147 | 11 |