Finite Group DatabasebetaFinite Group DatabasebetaOrder 11008.
566 conjugacy classes of subgroups; only the 113 normal subgroups are shown.
This group has 566 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×#14582719 | C2 | semidirect |
| 3. C2×#14582711 | C2 | semidirect |
| 4. #19136312 | C2 | semidirect |
| 5. #19136311 | C2 | semidirect |
| 6. #19134477 | C2 | semidirect |
| 7. C2×C43×#361 | C2 | semidirect |
| 13. #14583274 | C4 | semidirect |
| 46. #13063259 | D4 | semidirect |
| 65. #108×C43 | D4 | semidirect |
| 170. C2×#361 | D43 | semidirect |
| 198. C43 | #13261 | semidirect |
| 232. #108 | C22⋊D43 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#14583274 | 2 |
| C2×#14582719 | 2 |
| C2×#14582711 | 2 |
| #19136312 | 2 |
| #19136311 | 2 |
| #19134477 | 2 |
| C2×C43×#361 | 2 |
| #13261 | 43 |