Finite Group DatabasebetaFinite Group DatabasebetaOrder 11008.
466 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 466 conjugacy classes of subgroups — too many to draw. Only its 107 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×#14582711 | C2 | semidirect |
| 3. #19136330 | C2 | semidirect |
| 4. #19136322 | C2 | semidirect |
| 5. #19136310 | C2 | semidirect |
| 6. #19136200 | C2 | semidirect |
| 7. C43×#1833 | C2 | semidirect |
| 15. #14583283 | C4 | semidirect |
| 16. #14583276 | C4 | semidirect |
| 53. #13063265 | D4 | semidirect |
| 55. C2×C43⋊C16 | D4 | semidirect |
| 175. #1833 | D43 | semidirect |
| 201. C43 | #13215 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #19145081 | 2 |
| C2×#14582711 | 2 |
| #19136330 | 2 |
| #19136322 | 2 |
| #19136310 | 2 |
| #19136200 | 2 |
| C43×#1833 | 2 |
| #13215 | 43 |