Finite Group DatabasebetaFinite Group DatabasebetaOrder 11008.
252 conjugacy classes of subgroups; only the 71 normal subgroups are shown.
This group has 252 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. #19136852 | C2 | semidirect |
| 2. D4×C43⋊C16 | C2 | semidirect |
| 4. #19132668 | C2 | semidirect |
| 5. #19132644 | C2 | semidirect |
| 6. #19132640 | C2 | semidirect |
| 7. C43×#1669 | C2 | semidirect |
| 73. C43⋊C16 | D8 | semidirect |
| 79. D4×C43 | SD32 | semidirect |
| 115. #1669 | D43 | semidirect |
| 140. C43 | #12432 | semidirect |
| 202. D4 | #13063268 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #19136852 | 2 |
| D4×C43⋊C16 | 2 |
| #19133950 | 2 |
| #19132668 | 2 |
| #19132644 | 2 |
| #19132640 | 2 |
| C43×#1669 | 2 |
| #12432 | 43 |