Finite Group DatabasebetaFinite Group DatabasebetaOrder 11008.
458 conjugacy classes of subgroups; only the 71 normal subgroups are shown.
This group has 458 conjugacy classes of subgroups — too many to draw. Only its 71 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. D8×D172 | C2 | semidirect |
| 2. #19136844 | C2 | semidirect |
| 3. #19133947 | C2 | semidirect |
| 4. #19132642 | C2 | semidirect |
| 5. #19132556 | C2 | semidirect |
| 6. #19132549 | C2 | semidirect |
| 7. C43×#2206 | C2 | semidirect |
| 17. C4×C43⋊C16 | C22 | semidirect |
| 18. #14582652 | C22 | semidirect |
| 21. C43×#493 | C22 | semidirect |
| 23. C43×C4⋊C16 | C22 | semidirect |
| 77. D8×C43 | D8 | semidirect |
| 126. D172 | D16 | semidirect |
| 158. #2206 | D43 | semidirect |
| 175. #493 | C2×D43 | semidirect |
| 182. C4⋊C16 | C2×D43 | semidirect |
| 187. C43 | #12316 | semidirect |
| 245. D8 | #10621882 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D8×D172 | 2 |
| #19136844 | 2 |
| #19133947 | 2 |
| #19132642 | 2 |
| #19132556 | 2 |
| #19132549 | 2 |
| C43×#2206 | 2 |
| #12316 | 43 |