Finite Group DatabasebetaFinite Group DatabasebetaOrder 11008.
256 conjugacy classes of subgroups; only the 71 normal subgroups are shown.
This group has 256 conjugacy classes of subgroups — too many to draw. Only its 71 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. #19136742 | C2 | semidirect |
| 3. #19134187 | C2 | semidirect |
| 4. #19132659 | C2 | semidirect |
| 5. #19132654 | C2 | semidirect |
| 6. #19132640 | C2 | semidirect |
| 7. C8×D8×C43 | C2 | semidirect |
| 52. D8×C43 | SD16 | semidirect |
| 113. C8×D8 | D43 | semidirect |
| 137. C43 | #12418 | semidirect |
| 171. D8 | #10621873 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #19136742 | 2 |
| #19136630 | 2 |
| #19134187 | 2 |
| #19132659 | 2 |
| #19132654 | 2 |
| #19132640 | 2 |
| C8×D8×C43 | 2 |
| #12418 | 43 |