Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
1734 conjugacy classes of subgroups; only the 395 normal subgroups are shown.
This group has 1734 conjugacy classes of subgroups — too many to draw. Only its 395 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×#16810997 | C2 | semidirect |
| 3. C42×#88322 | C2 | semidirect |
| 4. C53×#2868 | C2 | semidirect |
| 19. C4×#88322 | D4 | semidirect |
| 34. C42×C53 | SD16 | semidirect |
| 48. #88322 | #127 | semidirect |
| 55. C4×C53 | #492 | semidirect |
| 58. #2868 | D53 | semidirect |
| 72. C53 | #33300 | semidirect |
| 96. C42 | #11719924 | semidirect |
| 114. C4 | #16810997 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16810997 | 2 |
| #20283110 | 2 |
| C42×#88322 | 2 |
| C53×#2868 | 2 |
| #33300 | 53 |