Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
176 conjugacy classes of subgroups; only the 65 normal subgroups are shown.
This group has 176 conjugacy classes of subgroups — too many to draw. Only its 65 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. #20276990 | C2 | semidirect |
| 3. #20272917 | C2 | semidirect |
| 5. C53×C4⋊C32 | C2 | semidirect |
| 19. D848 | Q8 | semidirect |
| 70. C4⋊C32 | D53 | semidirect |
| 85. C53 | #13705 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20276990 | 2 |
| C4×D848 | 2 |
| #20272917 | 2 |
| #20272894 | 2 |
| C53×C4⋊C32 | 2 |
| #13705 | 53 |