Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
298 conjugacy classes of subgroups; only the 144 normal subgroups are shown.
This group has 298 conjugacy classes of subgroups — too many to draw. Only its 144 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 |
|---|---|---|
| 3. #20289632 | C2 | semidirect |
| 24. #13133156 | C8 | semidirect |
| 45. C16×C53 | C2×C8 | semidirect |
| 46. #11719908 | C2×C8 | semidirect |
| 87. C53 | #11404 | semidirect |
| 118. C16 | D53⋊C8 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×#13133292 | 2 |
| #20289909 | 2 |
| #20289632 | 2 |
| C4×#13133156 | 2 |
| #11404 | 53 |