Finite Group DatabasebetaFinite Group DatabasebetaOrder 11008.
574 conjugacy classes of subgroups; only the 85 normal subgroups are shown.
This group has 574 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 |
|---|---|---|
| 2. #19135728 | C2 | semidirect |
| 3. #19135678 | C2 | semidirect |
| 4. #19132418 | C2 | semidirect |
| 5. #19132415 | C2 | semidirect |
| 6. #19132415 | C2 | semidirect |
| 7. C43×#2057 | C2 | semidirect |
| 109. C4⋊C4×C43 | SD16 | semidirect |
| 222. #2057 | D43 | semidirect |
| 256. C43 | #7752 | semidirect |
| 349. C4⋊C4 | #10621884 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #19140957 | 2 |
| #19135728 | 2 |
| #19135678 | 2 |
| #19132418 | 2 |
| #19132415 | 2 |
| C43×#2057 | 2 |
| #7752 | 43 |