Finite Group DatabasebetaFinite Group DatabasebetaOrder 11008.
240 conjugacy classes of subgroups; only the 85 normal subgroups are shown.
This group has 240 conjugacy classes of subgroups — too many to draw. Only its 85 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. #19133480 | C2 | semidirect |
| 2. D8×C43⋊C8 | C2 | semidirect |
| 3. #19132667 | C2 | semidirect |
| 4. #19132556 | C2 | semidirect |
| 5. #19132556 | C2 | semidirect |
| 6. #19132514 | C2 | semidirect |
| 51. D8×C43 | M16 | semidirect |
| 91. C43⋊C8 | D16 | semidirect |
| 134. C43 | #12069 | semidirect |
| 163. D8 | #10621877 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #19133480 | 2 |
| D8×C43⋊C8 | 2 |
| #19132667 | 2 |
| #19132556 | 2 |
| #19132514 | 2 |
| C4×D16×C43 | 2 |
| #12069 | 43 |