Finite Group DatabasebetaFinite Group DatabasebetaOrder 11008.
692 conjugacy classes of subgroups; only the 85 normal subgroups are shown.
This group has 692 conjugacy classes of subgroups — too many to draw. Only its 85 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. #19145584 | C2 | semidirect |
| 2. #19144687 | C2 | semidirect |
| 3. #19139529 | C2 | semidirect |
| 4. #19135513 | C2 | semidirect |
| 5. #19133194 | C2 | semidirect |
| 6. #19133037 | C2 | semidirect |
| 7. C43×#1285 | C2 | semidirect |
| 43. #13063325 | D4 | semidirect |
| 44. #13063322 | D4 | semidirect |
| 79. C4⋊C8×C43 | D4 | semidirect |
| 83. #97×C43 | D4 | semidirect |
| 237. #1285 | D43 | semidirect |
| 271. C43 | #10004 | semidirect |
| 311. C4⋊C8 | D172 | semidirect |
| 321. #97 | D172 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #19145584 | 2 |
| #19144687 | 2 |
| #19139529 | 2 |
| #19135513 | 2 |
| #19133194 | 2 |
| #19133037 | 2 |
| C43×#1285 | 2 |
| #10004 | 43 |