Finite Group DatabasebetaFinite Group DatabasebetaOrder 11008.
770 conjugacy classes of subgroups; only the 83 normal subgroups are shown.
This group has 770 conjugacy classes of subgroups — too many to draw. Only its 83 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. #19145048 | C2 | semidirect |
| 3. #19140701 | C2 | semidirect |
| 4. #19133308 | C2 | semidirect |
| 5. #19133194 | C2 | semidirect |
| 6. #19132488 | C2 | semidirect |
| 7. C43×#1505 | C2 | semidirect |
| 56. C4⋊(C43⋊C8) | D4 | semidirect |
| 61. #13063236 | D4 | semidirect |
| 64. C4⋊Q8×C43 | D4 | semidirect |
| 65. #127×C43 | D4 | semidirect |
| 210. #1505 | D43 | semidirect |
| 242. C43 | #10088 | semidirect |
| 256. C4⋊Q8 | D172 | semidirect |
| 262. #127 | D172 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #19145578 | 2 |
| #19145048 | 2 |
| #19140701 | 2 |
| #19133308 | 2 |
| #19133194 | 2 |
| #19132488 | 2 |
| C43×#1505 | 2 |
| #10088 | 43 |