Finite Group DatabasebetaFinite Group DatabasebetaOrder 11008.
458 conjugacy classes of subgroups; only the 79 normal subgroups are shown.
This group has 458 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. #19136844 | C2 | semidirect |
| 2. #19136630 | C2 | semidirect |
| 3. #19133950 | C2 | semidirect |
| 4. #19132641 | C2 | semidirect |
| 5. #19132556 | C2 | semidirect |
| 6. D4⋊(C43⋊C16) | C2 | semidirect |
| 7. D4×D8×C43 | C2 | semidirect |
| 10. #14583276 | C22 | semidirect |
| 12. C4⋊(C43⋊C16) | C22 | semidirect |
| 14. C4×C43⋊C16 | C22 | semidirect |
| 15. #14582652 | C22 | semidirect |
| 78. D8×C43 | D8 | semidirect |
| 114. D4×C43 | D16 | semidirect |
| 156. D4×D8 | D43 | semidirect |
| 187. C43 | #12316 | semidirect |
| 245. D8 | #10621882 | semidirect |
| 282. D4 | #13063266 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #19136844 | 2 |
| #19136630 | 2 |
| #19133950 | 2 |
| #19132641 | 2 |
| #19132556 | 2 |
| D4⋊(C43⋊C16) | 2 |
| D4×D8×C43 | 2 |
| #12316 | 43 |