Finite Group DatabasebetaFinite Group DatabasebetaOrder 11008.
442 conjugacy classes of subgroups; only the 79 normal subgroups are shown.
This group has 442 conjugacy classes of subgroups — too many to draw. Only its 79 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. #19136850 | C2 | semidirect |
| 2. #19136640 | C2 | semidirect |
| 3. #19133960 | C2 | semidirect |
| 4. #19132641 | C2 | semidirect |
| 5. #19132556 | C2 | semidirect |
| 6. D4⋊(C43⋊C16) | C2 | semidirect |
| 10. #14583279 | C22 | semidirect |
| 12. C4⋊(C43⋊C16) | C22 | semidirect |
| 14. C4×C43⋊C16 | C22 | semidirect |
| 15. #14582652 | C22 | semidirect |
| 112. D4×C43 | SD32 | semidirect |
| 180. C43 | #12320 | semidirect |
| 270. D4 | #13063269 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #19136850 | 2 |
| #19136640 | 2 |
| #19133960 | 2 |
| #19132641 | 2 |
| #19132556 | 2 |
| D4⋊(C43⋊C16) | 2 |
| D4×D8×C43 | 2 |
| #12320 | 43 |