Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
708 conjugacy classes of subgroups; only the 144 normal subgroups are shown.
This group has 708 conjugacy classes of subgroups — too many to draw. Only its 144 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 |
|---|---|---|
| 2. C4⋊C8×#6157 | C2 | semidirect |
| 4. #20289594 | C2 | semidirect |
| 15. #16811481 | C4 | semidirect |
| 18. #16810367 | C4 | semidirect |
| 19. #16810366 | C4 | semidirect |
| 20. C53×#331 | C4 | semidirect |
| 34. #13133284 | C2×C4 | semidirect |
| 44. C4⋊#88322 | C2×C4 | semidirect |
| 47. C4⋊C8×C53 | C2×C4 | semidirect |
| 145. #6157 | #331 | direct (N × H) |
| 178. #331 | #6157 | direct (N × H) |
| 179. C53 | C4×#331 | semidirect |
| 205. C4⋊C8 | C2×#6157 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #127×#6157 | 2 |
| C4⋊C8×#6157 | 2 |
| D53⋊#331 | 2 |
| #20289594 | 2 |
| #331×D53 | 2 |
| C4×#331 | 53 |