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. #19145578 | C2 | semidirect |
| 2. #19139534 | C2 | semidirect |
| 3. #19135515 | C2 | semidirect |
| 4. #19133194 | C2 | semidirect |
| 5. #19133038 | C2 | semidirect |
| 6. #19132450 | C2 | semidirect |
| 7. C43×#3109 | C2 | semidirect |
| 52. C4⋊(C43⋊C8) | D4 | semidirect |
| 65. C4⋊Q8×C43 | D4 | semidirect |
| 66. #127×C43 | D4 | semidirect |
| 84. #97×C43 | D4 | semidirect |
| 232. #3109 | D43 | semidirect |
| 271. C43 | #10004 | semidirect |
| 282. C4⋊Q8 | C22⋊D43 | semidirect |
| 283. #127 | C22⋊D43 | semidirect |
| 321. #97 | C22⋊D43 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #19145578 | 2 |
| #19139534 | 2 |
| #19135515 | 2 |
| #19133194 | 2 |
| #19133038 | 2 |
| #19132450 | 2 |
| C43×#3109 | 2 |
| #10004 | 43 |