Finite Group DatabasebetaFinite Group DatabasebetaOrder 11008.
566 conjugacy classes of subgroups; only the 121 normal subgroups are shown.
This group has 566 conjugacy classes of subgroups — too many to draw. Only its 121 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×#14582701 | C2 | semidirect |
| 3. C2×#14582701 | C2 | semidirect |
| 4. #19135328 | C2 | semidirect |
| 5. C43×#1374 | C2 | semidirect |
| 37. #13063259 | D4 | semidirect |
| 146. #1374 | D43 | semidirect |
| 167. C43 | #13407 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#14583276 | 2 |
| C2×#14582701 | 2 |
| #19135328 | 2 |
| C43×#1374 | 2 |
| #13407 | 43 |