Finite Group DatabasebetaFinite Group DatabasebetaOrder 11008.
326 conjugacy classes of subgroups; only the 95 normal subgroups are shown.
This group has 326 conjugacy classes of subgroups — too many to draw. Only its 95 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. #19136393 | C2 | semidirect |
| 3. C4×#13063264 | C2 | semidirect |
| 4. #19132575 | C2 | semidirect |
| 5. #19132573 | C2 | semidirect |
| 6. D4⋊(C43⋊C16) | C2 | semidirect |
| 7. C43×D4⋊C16 | C2 | semidirect |
| 155. D4⋊C16 | D43 | semidirect |
| 180. C43 | #11614 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #19143567 | 2 |
| #19136393 | 2 |
| C4×#13063264 | 2 |
| #19132575 | 2 |
| #19132573 | 2 |
| D4⋊(C43⋊C16) | 2 |
| C43×D4⋊C16 | 2 |
| #11614 | 43 |