Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
9486 conjugacy classes of subgroups; only the 3915 normal subgroups are shown.
This group has 9486 conjugacy classes of subgroups — too many to draw. Only its 3915 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×#13133211 | C2 | direct (N × H) |
| 2. C23×#11719919 | C2 | semidirect |
| 4. C23×C42×C53 | C2 | semidirect |
| 7. C2×#13133211 | C22 | direct (N × H) |
| 8. C22×#11719919 | C22 | semidirect |
| 11. C22×C42×C53 | C22 | semidirect |
| 16. #13133211 | C23 | direct (N × H) |
| 17. C2×#11719919 | C23 | semidirect |
| 22. C2×C42×C53 | C23 | semidirect |
| 32. C42×C53 | C24 | semidirect |
| 34. #11719919 | C24 | semidirect |
| 35. C23×C53 | #126 | semidirect |
| 46. C22×C53 | C2×#126 | semidirect |
| 56. C23×C42 | D53 | semidirect |
| 57. C2×C53 | C22×#126 | semidirect |
| 66. C22×C42 | C2×D53 | semidirect |
| 67. C53 | C23×#126 | semidirect |
| 78. C2×C42 | C22×D53 | semidirect |
| 90. C42 | C23×D53 | semidirect |
| 94. C23 | #13133211 | direct (N × H) |
| 103. C22 | C2×#13133211 | direct (N × H) |
| 109. C2 | C22×#13133211 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#13133211 | 2 |
| C23×#11719919 | 2 |
| C23×#11719921 | 2 |
| C23×C42×C53 | 2 |
| C23×#126 | 53 |