Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
4070 conjugacy classes of subgroups; only the 427 normal subgroups are shown.
This group has 4070 conjugacy classes of subgroups — too many to draw. Only its 427 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. C2×C22⋊C8×D53 | C2 | semidirect |
| 3. #20274627 | C2 | semidirect |
| 4. #20274626 | C2 | semidirect |
| 5. C53×#1780 | C2 | semidirect |
| 14. C2×C22⋊#88322 | C22 | semidirect |
| 15. C2×#13133129 | C22 | semidirect |
| 18. C2×C22⋊C8×C53 | C22 | semidirect |
| 141. #1780 | D53 | direct (N × H) |
| 146. D53 | #1780 | direct (N × H) |
| 159. C2×C22⋊C8 | C2×D53 | semidirect |
| 160. C53 | C2×#1780 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#41×D53 | 2 |
| C2×C22⋊C8×D53 | 2 |
| #20274627 | 2 |
| #20274626 | 2 |
| C53×#1780 | 2 |
| C2×#1780 | 53 |