Finite Group DatabasebetaFinite Group DatabasebetaOrder 11008.
568 conjugacy classes of subgroups; only the 95 normal subgroups are shown.
This group has 568 conjugacy classes of subgroups — too many to draw. Only its 95 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. #19147731 | C2 | semidirect |
| 2. #19144176 | C2 | semidirect |
| 3. #19136332 | C2 | semidirect |
| 4. #19132697 | C2 | semidirect |
| 5. C43×#2112 | C2 | semidirect |
| 26. C2×Dic172 | D4 | semidirect |
| 28. C2×D344 | D4 | semidirect |
| 39. #13063257 | D4 | semidirect |
| 52. C2×C16×C43 | D4 | semidirect |
| 141. #2112 | D43 | semidirect |
| 163. C43 | #13309 | semidirect |
| 191. C2×C16 | C22⋊D43 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #19147731 | 2 |
| #19144176 | 2 |
| #19136332 | 2 |
| #19132697 | 2 |
| C43×#2112 | 2 |
| #13309 | 43 |