Finite Group DatabasebetaFinite Group DatabasebetaOrder 11008.
334 conjugacy classes of subgroups; only the 61 normal subgroups are shown.
This group has 334 conjugacy classes of subgroups — too many to draw. Only its 61 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. C2×D16×D43 | C2 | semidirect |
| 2. C2×#14582734 | C2 | semidirect |
| 3. #19136678 | C2 | semidirect |
| 4. #19132774 | C2 | semidirect |
| 5. #19132773 | C2 | semidirect |
| 6. (C2×D43)⋊C32 | C2 | semidirect |
| 7. C2×C43×D32 | C2 | semidirect |
| 16. C2×C43⋊C32 | C22 | semidirect |
| 17. #14582725 | C22 | semidirect |
| 20. C2×D16×C43 | C22 | semidirect |
| 22. C2×C32×C43 | C22 | semidirect |
| 31. D688 | D4 | semidirect |
| 44. D16×C43 | D4 | semidirect |
| 109. C2×D43 | D32 | semidirect |
| 116. C2×D32 | D43 | semidirect |
| 134. C2×D16 | C2×D43 | semidirect |
| 140. C2×C32 | C2×D43 | semidirect |
| 143. C43 | #13661 | semidirect |
| 159. D16 | C22⋊D43 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×D16×D43 | 2 |
| C2×#14582734 | 2 |
| #19136678 | 2 |
| #19132774 | 2 |
| #19132773 | 2 |
| (C2×D43)⋊C32 | 2 |
| C2×C43×D32 | 2 |
| #13661 | 43 |