Finite Group DatabasebetaFinite Group DatabasebetaOrder 11008.
214 conjugacy classes of subgroups; only the 75 normal subgroups are shown.
This group has 214 conjugacy classes of subgroups — too many to draw. Only its 75 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. C4×D688 | C2 | semidirect |
| 3. #19132794 | C2 | semidirect |
| 4. #19132773 | C2 | semidirect |
| 5. #19132772 | C2 | semidirect |
| 6. C4×C43⋊C32 | C2 | semidirect |
| 7. C4×D16×C43 | C2 | semidirect |
| 10. #14582734 | C4 | direct (N × H) |
| 23. D688 | C2×C4 | semidirect |
| 27. C43⋊C32 | C2×C4 | semidirect |
| 31. D16×C43 | C2×C4 | semidirect |
| 81. C4×C43 | D32 | semidirect |
| 87. C4×D16 | D43 | semidirect |
| 109. C43 | C4×D32 | semidirect |
| 117. D16 | C4×D43 | semidirect |
| 171. C4 | #14582734 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#14582734 | 2 |
| C4×D688 | 2 |
| #19132794 | 2 |
| #19132773 | 2 |
| #19132772 | 2 |
| C4×C43⋊C32 | 2 |
| C4×D16×C43 | 2 |
| C4×D32 | 43 |