Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
424 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 424 conjugacy classes of subgroups — too many to draw. Only its 107 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 |
|---|---|---|
| 2. #20276504 | C2 | semidirect |
| 5. #20275501 | C2 | semidirect |
| 6. #20272803 | C2 | semidirect |
| 7. C53×#1382 | C2 | semidirect |
| 20. #16810435 | C4 | semidirect |
| 42. #13133157 | C2×C4 | semidirect |
| 59. #108×C53 | C2×C4 | semidirect |
| 159. #1382 | D53 | semidirect |
| 185. C53 | #12940 | semidirect |
| 211. #108 | C4×D53 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20283566 | 2 |
| #20276504 | 2 |
| C2×#16810435 | 2 |
| C2×#16810425 | 2 |
| #20275501 | 2 |
| #20272803 | 2 |
| C53×#1382 | 2 |
| #12940 | 53 |