Finite Group DatabasebetaFinite Group DatabasebetaOrder 11008.
398 conjugacy classes of subgroups; only the 75 normal subgroups are shown.
This group has 398 conjugacy classes of subgroups — too many to draw. Only its 75 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. #19140243 | C2 | semidirect |
| 4. #19132488 | C2 | semidirect |
| 5. #19132461 | C2 | semidirect |
| 6. #19132452 | C2 | semidirect |
| 52. C4⋊Q8×C43 | Q8 | semidirect |
| 53. #127×C43 | Q8 | semidirect |
| 208. C43 | #10378 | semidirect |
| 212. C4⋊Q8 | Dic86 | semidirect |
| 213. #127 | Dic86 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #19140243 | 2 |
| #19135515 | 2 |
| #19133142 | 2 |
| #19132488 | 2 |
| #19132461 | 2 |
| #19132452 | 2 |
| C43×#1505 | 2 |
| #10378 | 43 |