Finite Group DatabasebetaFinite Group DatabasebetaOrder 11008.
406 conjugacy classes of subgroups; only the 67 normal subgroups are shown.
This group has 406 conjugacy classes of subgroups — too many to draw. Only its 67 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. #19136671 | C2 | semidirect |
| 2. #19134209 | C2 | semidirect |
| 3. #19132632 | C2 | semidirect |
| 4. #19132568 | C2 | semidirect |
| 5. C43×#3292 | C2 | semidirect |
| 7. #14583276 | C22 | semidirect |
| 9. #14582720 | C22 | semidirect |
| 11. C8×C43⋊C8 | C22 | semidirect |
| 45. Q16×C43 | D8 | semidirect |
| 51. D8×C43 | D8 | semidirect |
| 92. #3292 | D43 | semidirect |
| 113. C43 | #12310 | semidirect |
| 142. Q16 | #10621882 | semidirect |
| 151. D8 | #10621882 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #19136671 | 2 |
| #19134209 | 2 |
| #19132632 | 2 |
| #19132568 | 2 |
| C43×#3292 | 2 |
| #12310 | 43 |