Finite Group DatabasebetaFinite Group DatabasebetaOrder 11008.
738 conjugacy classes of subgroups; only the 155 normal subgroups are shown.
This group has 738 conjugacy classes of subgroups — too many to draw. Only its 155 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. #19135543 | C2 | semidirect |
| 4. #19132436 | C2 | semidirect |
| 9. #14583271 | C4 | semidirect |
| 28. #13063325 | C2×C4 | semidirect |
| 33. C4×C43⋊C8 | C2×C4 | semidirect |
| 74. C4⋊C4×C43 | SD16 | semidirect |
| 172. C43 | #9064 | semidirect |
| 236. C4⋊C4 | #10621883 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#14583271 | 2 |
| #19135543 | 2 |
| C2×#14582643 | 2 |
| #19132436 | 2 |
| C43×#2366 | 2 |
| #9064 | 43 |