Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
542 conjugacy classes of subgroups; only the 105 normal subgroups are shown.
This group has 542 conjugacy classes of subgroups — too many to draw. Only its 105 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. #20285239 | C2 | semidirect |
| 4. #20273280 | C2 | semidirect |
| 5. C53×#1281 | C2 | semidirect |
| 63. C2×C8×C53 | SD16 | semidirect |
| 121. #1281 | D53 | semidirect |
| 141. C53 | #10220 | semidirect |
| 186. C2×C8 | #11719913 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20285658 | 2 |
| #20285239 | 2 |
| #20275539 | 2 |
| #20273280 | 2 |
| C53×#1281 | 2 |
| #10220 | 53 |