Finite Group DatabasebetaFinite Group DatabasebetaOrder 11008.
486 conjugacy classes of subgroups; only the 109 normal subgroups are shown.
This group has 486 conjugacy classes of subgroups — too many to draw. Only its 109 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. #19147697 | C2 | semidirect |
| 3. C2×#14582712 | C2 | semidirect |
| 4. #19134642 | C2 | semidirect |
| 5. #19132710 | C2 | semidirect |
| 6. #19132709 | C2 | semidirect |
| 7. C2×C43×#361 | C2 | semidirect |
| 41. #13063265 | D4 | semidirect |
| 62. M32×C43 | D4 | semidirect |
| 166. C2×#361 | D43 | semidirect |
| 194. C43 | #13079 | semidirect |
| 222. M32 | C22⋊D43 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #19147697 | 2 |
| #19144239 | 2 |
| C2×#14582712 | 2 |
| #19134642 | 2 |
| #19132710 | 2 |
| #19132709 | 2 |
| C2×C43×#361 | 2 |
| #13079 | 43 |