Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
2046 conjugacy classes of subgroups; only the 395 normal subgroups are shown.
This group has 2046 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×#16810999 | C2 | semidirect |
| 2. #20283110 | C2 | semidirect |
| 3. C42×#88322 | C2 | semidirect |
| 4. C53×#2867 | C2 | semidirect |
| 19. C4×#88322 | D4 | semidirect |
| 36. C42×C53 | D8 | semidirect |
| 52. #88322 | #127 | semidirect |
| 60. C4×C53 | #493 | semidirect |
| 64. #2867 | D53 | semidirect |
| 78. C53 | #33301 | semidirect |
| 104. C42 | #11719922 | semidirect |
| 125. C4 | #16810999 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16810999 | 2 |
| #20283110 | 2 |
| C42×#88322 | 2 |
| C53×#2867 | 2 |
| #33301 | 53 |