Finite Group DatabasebetaFinite Group DatabasebetaOrder 11008.
540 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 540 conjugacy classes of subgroups — too many to draw. Only its 99 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. #19136310 | C2 | semidirect |
| 4. #19132677 | C2 | semidirect |
| 5. C43×#1945 | C2 | semidirect |
| 40. #107×C43 | D4 | semidirect |
| 117. #1945 | D43 | semidirect |
| 136. C43 | #13413 | semidirect |
| 159. #107 | D172 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#14583276 | 2 |
| C2×#14582711 | 2 |
| #19136310 | 2 |
| #19132677 | 2 |
| C43×#1945 | 2 |
| #13413 | 43 |