Finite Group DatabasebetaFinite Group DatabasebetaOrder 11008.
412 conjugacy classes of subgroups; only the 113 normal subgroups are shown.
This group has 412 conjugacy classes of subgroups — too many to draw. Only its 113 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. C2×#14582721 | C2 | semidirect |
| 4. #19135321 | C2 | semidirect |
| 5. #19132694 | C2 | semidirect |
| 6. #19132676 | C2 | semidirect |
| 18. #14582709 | C4 | semidirect |
| 72. Q16×C43 | C4⋊C4 | semidirect |
| 76. D8×C43 | C4⋊C4 | semidirect |
| 180. C43 | #12950 | semidirect |
| 229. Q16 | Dic43⋊C4 | semidirect |
| 233. D8 | Dic43⋊C4 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#14583016 | 2 |
| C2×#14582721 | 2 |
| C2×#14582709 | 2 |
| #19135321 | 2 |
| #19132694 | 2 |
| #19132676 | 2 |
| C2×C43×#360 | 2 |
| #12950 | 43 |