Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
13310 conjugacy classes of subgroups; only the 6264 normal subgroups are shown.
This group has 13310 conjugacy classes of subgroups — too many to draw. Only its 6264 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. C23×#11719936 | C2 | direct (N × H) |
| 2. C24×#88324 | C2 | semidirect |
| 4. C22×#11719936 | C22 | direct (N × H) |
| 5. C23×#88324 | C22 | semidirect |
| 11. C2×#11719936 | C23 | direct (N × H) |
| 12. C22×#88324 | C23 | semidirect |
| 21. C24×C53 | M16 | semidirect |
| 30. C2×#88324 | C24 | semidirect |
| 31. #11719936 | C24 | direct (N × H) |
| 32. C23×C53 | C2×M16 | semidirect |
| 41. #88324 | C25 | semidirect |
| 43. C22×C53 | C22×M16 | semidirect |
| 53. C2×C53 | C23×M16 | semidirect |
| 63. C53 | C24×M16 | semidirect |
| 76. C24 | #11719936 | direct (N × H) |
| 87. C23 | C2×#11719936 | direct (N × H) |
| 97. C22 | C22×#11719936 | direct (N × H) |
| 103. C2 | C23×#11719936 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×#11719936 | 2 |
| C24×#88324 | 2 |
| C24×C4×D53 | 2 |
| C24×M16 | 53 |