Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
840 conjugacy classes of subgroups; only the 111 normal subgroups are shown.
This group has 840 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×#16810410 | C2 | semidirect |
| 2. #20274703 | C2 | semidirect |
| 3. C4×#13133134 | C2 | semidirect |
| 12. C23×D4×C53 | C4 | semidirect |
| 19. C53×#380 | C4 | semidirect |
| 20. C53×#379 | C4 | semidirect |
| 25. #13133134 | D4 | semidirect |
| 197. C4×C53 | AΣL(1,𝔽16) | semidirect |
| 212. C23×D4 | Dic53 | semidirect |
| 223. #380 | Dic53 | semidirect |
| 224. #379 | Dic53 | semidirect |
| 228. C53 | #13218 | semidirect |
| 405. C4 | #16810410 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16810410 | 2 |
| #20274703 | 2 |
| C4×#13133134 | 2 |
| C53×#2408 | 2 |
| #13218 | 53 |