Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
828 conjugacy classes of subgroups; only the 131 normal subgroups are shown.
This group has 828 conjugacy classes of subgroups — too many to draw. Only its 131 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×#16810815 | C2 | semidirect |
| 2. #20279631 | C2 | semidirect |
| 3. C2×#16810352 | C2 | semidirect |
| 4. #20272598 | C2 | semidirect |
| 5. C53×#1957 | C2 | semidirect |
| 37. C4⋊#88322 | D4 | semidirect |
| 45. #127×C53 | D4 | semidirect |
| 74. C2×D212 | D8 | semidirect |
| 172. #1957 | D53 | semidirect |
| 196. C53 | #10228 | semidirect |
| 209. #127 | D212 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16810815 | 2 |
| #20279631 | 2 |
| C2×#16810352 | 2 |
| #20272598 | 2 |
| C53×#1957 | 2 |
| #10228 | 53 |