Finite Group DatabasebetaFinite Group DatabasebetaOrder 11008.
476 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 476 conjugacy classes of subgroups — too many to draw. Only its 117 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. #19143512 | C2 | semidirect |
| 2. C2×#14582712 | C2 | semidirect |
| 3. #19136323 | C2 | semidirect |
| 4. #19135506 | C2 | semidirect |
| 5. #19132699 | C2 | semidirect |
| 6. #19132680 | C2 | semidirect |
| 24. C2×SD32×C43 | C4 | semidirect |
| 25. C2×D16×C43 | C4 | semidirect |
| 183. C2×SD32 | Dic43 | semidirect |
| 184. C2×D16 | Dic43 | semidirect |
| 197. C43 | #13036 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #19143512 | 2 |
| C2×#14582712 | 2 |
| #19136323 | 2 |
| #19135506 | 2 |
| #19132699 | 2 |
| #19132680 | 2 |
| C2×C43×#509 | 2 |
| #13036 | 43 |