Finite Group DatabasebetaFinite Group DatabasebetaOrder 11008.
552 conjugacy classes of subgroups; only the 101 normal subgroups are shown.
This group has 552 conjugacy classes of subgroups — too many to draw. Only its 101 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. #19147729 | C2 | semidirect |
| 2. #19136323 | C2 | semidirect |
| 3. #19135488 | C2 | semidirect |
| 4. #19132675 | C2 | semidirect |
| 5. C43×#3150 | C2 | semidirect |
| 26. C2×Dic172 | D4 | semidirect |
| 28. C2×D344 | D4 | semidirect |
| 36. C2×C43⋊C16 | D4 | semidirect |
| 159. #3150 | D43 | semidirect |
| 186. C43 | #13340 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #19147729 | 2 |
| #19136323 | 2 |
| #19135488 | 2 |
| #19132675 | 2 |
| C43×#3150 | 2 |
| #13340 | 43 |