Finite Group DatabasebetaFinite Group DatabasebetaOrder 11008.
458 conjugacy classes of subgroups; only the 73 normal subgroups are shown.
This group has 458 conjugacy classes of subgroups — too many to draw. Only its 73 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. D4×D344 | C2 | semidirect |
| 2. #19136845 | C2 | semidirect |
| 3. #19136631 | C2 | semidirect |
| 4. #19133950 | C2 | semidirect |
| 5. #19132642 | C2 | semidirect |
| 6. #19132557 | C2 | semidirect |
| 7. C43×D4⋊C16 | C2 | semidirect |
| 13. #14583276 | C22 | semidirect |
| 20. #14582652 | C22 | semidirect |
| 23. C43×C4⋊C16 | C22 | semidirect |
| 24. C4×C16×C43 | C22 | semidirect |
| 94. D344 | D8 | semidirect |
| 105. D4×C43 | D16 | semidirect |
| 162. D4⋊C16 | D43 | semidirect |
| 182. C4⋊C16 | C2×D43 | semidirect |
| 184. C4×C16 | C2×D43 | semidirect |
| 187. C43 | #12316 | semidirect |
| 282. D4 | D688 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D4×D344 | 2 |
| #19136845 | 2 |
| #19136631 | 2 |
| #19133950 | 2 |
| #19132642 | 2 |
| #19132557 | 2 |
| C43×D4⋊C16 | 2 |
| #12316 | 43 |