Finite Group DatabasebetaFinite Group DatabasebetaOrder 11008.
844 conjugacy classes of subgroups; only the 111 normal subgroups are shown.
This group has 844 conjugacy classes of subgroups — too many to draw. Only its 111 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. C2×#14582686 | C2 | semidirect |
| 2. #19134587 | C2 | semidirect |
| 3. C4×#13063240 | C2 | semidirect |
| 12. C23×D4×C43 | C4 | semidirect |
| 19. C43×#380 | C4 | semidirect |
| 20. C43×#379 | C4 | semidirect |
| 28. #13063240 | D4 | semidirect |
| 195. C4×C43 | AΣL(1,𝔽16) | semidirect |
| 209. C23×D4 | Dic43 | semidirect |
| 219. #380 | Dic43 | semidirect |
| 220. #379 | Dic43 | semidirect |
| 225. C43 | #13221 | semidirect |
| 400. C4 | #14582686 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#14582686 | 2 |
| #19134587 | 2 |
| C4×#13063240 | 2 |
| C43×#2408 | 2 |
| #13221 | 43 |