Finite Group DatabasebetaFinite Group DatabasebetaOrder 11008.
662 conjugacy classes of subgroups; only the 81 normal subgroups are shown.
This group has 662 conjugacy classes of subgroups — too many to draw. Only its 81 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. #19145059 | C2 | semidirect |
| 2. #19144686 | C2 | semidirect |
| 3. #19133219 | C2 | semidirect |
| 4. #19133141 | C2 | semidirect |
| 5. #19133038 | C2 | semidirect |
| 6. #19132459 | C2 | semidirect |
| 7. C43×#2631 | C2 | semidirect |
| 42. #13063325 | D4 | semidirect |
| 43. #13063322 | D4 | semidirect |
| 58. #13063236 | D4 | semidirect |
| 59. C4×C43⋊C8 | D4 | semidirect |
| 223. #2631 | D43 | semidirect |
| 260. C43 | #10018 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #19145059 | 2 |
| #19144686 | 2 |
| #19133219 | 2 |
| #19133141 | 2 |
| #19133038 | 2 |
| #19132459 | 2 |
| C43×#2631 | 2 |
| #10018 | 43 |