Finite Group DatabasebetaFinite Group DatabasebetaOrder 11008.
686 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 686 conjugacy classes of subgroups — too many to draw. Only its 99 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. #19144596 | C2 | semidirect |
| 2. #19144061 | C2 | semidirect |
| 3. #19139497 | C2 | semidirect |
| 4. #19133154 | C2 | semidirect |
| 5. #19133019 | C2 | semidirect |
| 6. #19132987 | C2 | semidirect |
| 7. C43×#1286 | C2 | semidirect |
| 44. #13063325 | D4 | semidirect |
| 45. #13063322 | D4 | semidirect |
| 81. C4⋊C8×C43 | D4 | semidirect |
| 83. C4×C8×C43 | D4 | semidirect |
| 113. C2×D172 | D8 | semidirect |
| 255. #1286 | D43 | semidirect |
| 289. C43 | #9996 | semidirect |
| 331. C4⋊C8 | D172 | semidirect |
| 339. C4×C8 | D172 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #19144596 | 2 |
| #19144061 | 2 |
| #19139497 | 2 |
| #19133154 | 2 |
| #19133019 | 2 |
| #19132987 | 2 |
| C43×#1286 | 2 |
| #9996 | 43 |