Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
1164 conjugacy classes of subgroups; only the 131 normal subgroups are shown.
This group has 1164 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×#16810390 | C2 | semidirect |
| 2. C2×#16810347 | C2 | semidirect |
| 3. #20272712 | C2 | direct (N × H) |
| 8. #16810390 | C22 | semidirect |
| 10. #16810347 | C22 | semidirect |
| 12. C23×D4×C53 | C4 | semidirect |
| 17. C53×#392 | C4 | semidirect |
| 19. C2×#95×C53 | C4 | semidirect |
| 40. C22×D4×C53 | C2×C4 | semidirect |
| 54. #95×C53 | C2×C4 | semidirect |
| 248. C2×C53 | #1343 | semidirect |
| 253. C23×D4 | Dic53 | semidirect |
| 260. #392 | Dic53 | semidirect |
| 262. C2×#95 | Dic53 | semidirect |
| 267. C53 | C2×#1343 | semidirect |
| 280. C22×D4 | C2×Dic53 | semidirect |
| 302. #95 | C2×Dic53 | semidirect |
| 491. C2 | #20272712 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16810390 | 2 |
| C2×#16810347 | 2 |
| #20272712 | 2 |
| C2×C53×#392 | 2 |
| C2×#1343 | 53 |