Finite Group DatabasebetaFinite Group DatabasebetaOrder 11008.
542 conjugacy classes of subgroups; only the 171 normal subgroups are shown.
This group has 542 conjugacy classes of subgroups — too many to draw. Only its 171 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×D688 | C2 | semidirect |
| 2. C2×#14582734 | C2 | direct (N × H) |
| 3. C22×C43⋊C32 | C2 | semidirect |
| 4. C22×D16×C43 | C2 | semidirect |
| 7. C2×D688 | C22 | semidirect |
| 8. #14582734 | C22 | direct (N × H) |
| 9. C2×C43⋊C32 | C22 | semidirect |
| 12. C2×D16×C43 | C22 | semidirect |
| 18. D688 | C23 | semidirect |
| 19. C43⋊C32 | C23 | semidirect |
| 25. D16×C43 | C23 | semidirect |
| 59. C22×C43 | D32 | semidirect |
| 66. C22×D16 | D43 | semidirect |
| 70. C2×C43 | C2×D32 | semidirect |
| 78. C2×D16 | C2×D43 | semidirect |
| 82. C43 | C22×D32 | semidirect |
| 93. D16 | C22×D43 | semidirect |
| 129. C22 | #14582734 | direct (N × H) |
| 135. C2 | C2×#14582734 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×D688 | 2 |
| C2×#14582734 | 2 |
| C22×C43⋊C32 | 2 |
| C22×D16×C43 | 2 |
| C22×D32 | 43 |