Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
11422 conjugacy classes of subgroups; only the 5752 normal subgroups are shown.
This group has 11422 conjugacy classes of subgroups — too many to draw. Only its 5752 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. C22×#13133305 | C2 | direct (N × H) |
| 2. C23×#11719936 | C2 | semidirect |
| 3. C23×D53⋊C8 | C2 | semidirect |
| 5. C2×#13133305 | C22 | direct (N × H) |
| 6. C22×#11719936 | C22 | semidirect |
| 7. C22×D53⋊C8 | C22 | semidirect |
| 15. #13133305 | C23 | direct (N × H) |
| 16. C2×#11719936 | C23 | semidirect |
| 17. C2×D53⋊C8 | C23 | semidirect |
| 43. #11719936 | C24 | semidirect |
| 44. D53⋊C8 | C24 | semidirect |
| 45. C23×C53 | #131 | semidirect |
| 59. C22×C53 | C2×#131 | semidirect |
| 70. C2×C53 | C22×#131 | semidirect |
| 83. C53 | C23×#131 | semidirect |
| 116. C23 | #13133305 | direct (N × H) |
| 129. C22 | C2×#13133305 | direct (N × H) |
| 135. C2 | C22×#13133305 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#13133305 | 2 |
| C23×#11719936 | 2 |
| C23×D53⋊C8 | 2 |
| C23×#11719949 | 2 |
| C23×#131 | 53 |