Finite Group DatabasebetaFinite Group DatabasebetaOrder 11008.
518 conjugacy classes of subgroups; only the 111 normal subgroups are shown.
This group has 518 conjugacy classes of subgroups — too many to draw. Only its 111 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. C4⋊C16×D43 | C2 | semidirect |
| 3. #335×D43 | C2 | semidirect |
| 4. #19132642 | C2 | semidirect |
| 5. #19132641 | C2 | semidirect |
| 6. #19132640 | C2 | semidirect |
| 7. C43×#1361 | C2 | semidirect |
| 18. C4⋊(C43⋊C16) | C22 | semidirect |
| 20. #14582652 | C22 | semidirect |
| 23. C43×C4⋊C16 | C22 | semidirect |
| 24. C43×#335 | C22 | semidirect |
| 161. #1361 | D43 | direct (N × H) |
| 167. D43 | #1361 | direct (N × H) |
| 181. C4⋊C16 | C2×D43 | semidirect |
| 184. #335 | C2×D43 | semidirect |
| 185. C43 | C2×#1361 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #493×D43 | 2 |
| C4⋊C16×D43 | 2 |
| #335×D43 | 2 |
| #19132642 | 2 |
| #19132641 | 2 |
| #19132640 | 2 |
| C43×#1361 | 2 |
| C2×#1361 | 43 |