Finite Group DatabasebetaFinite Group DatabasebetaOrder 11008.
338 conjugacy classes of subgroups; only the 71 normal subgroups are shown.
This group has 338 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. D8×Dic86 | C2 | semidirect |
| 2. #19136818 | C2 | semidirect |
| 3. #19133952 | C2 | semidirect |
| 4. #19132649 | C2 | semidirect |
| 5. #19132573 | C2 | semidirect |
| 6. #19132556 | C2 | semidirect |
| 68. D8×C43 | SD16 | semidirect |
| 109. Dic86 | D16 | semidirect |
| 161. C43 | #12352 | semidirect |
| 206. D8 | #10621883 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D8×Dic86 | 2 |
| #19136818 | 2 |
| #19133952 | 2 |
| #19132649 | 2 |
| #19132573 | 2 |
| #19132556 | 2 |
| C43×#2206 | 2 |
| #12352 | 43 |