Finite Group DatabasebetaFinite Group DatabasebetaOrder 11008.
454 conjugacy classes of subgroups; only the 95 normal subgroups are shown.
This group has 454 conjugacy classes of subgroups — too many to draw. Only its 95 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. #19142971 | C2 | semidirect |
| 4. #19132454 | C2 | semidirect |
| 5. #19132453 | C2 | semidirect |
| 6. #19132427 | C2 | semidirect |
| 44. C4⋊Q8×C43 | Q8 | semidirect |
| 45. #127×C43 | Q8 | semidirect |
| 193. C43 | #10362 | semidirect |
| 199. C4⋊Q8 | Dic86 | semidirect |
| 200. #127 | Dic86 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #19142971 | 2 |
| #19135424 | 2 |
| #19133155 | 2 |
| #19132454 | 2 |
| #19132453 | 2 |
| #19132427 | 2 |
| C43×#1517 | 2 |
| #10362 | 43 |