Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
5502 conjugacy classes of subgroups; only the 2056 normal subgroups are shown.
This group has 5502 conjugacy classes of subgroups — too many to draw. Only its 2056 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×#16811569 | C2 | direct (N × H) |
| 7. #16811569 | C22 | direct (N × H) |
| 9. C22×C4×Dic53 | C4 | semidirect |
| 10. C2×C42×D53 | C4 | semidirect |
| 12. C22×C42×C53 | C4 | semidirect |
| 23. C2×C4×Dic53 | C2×C4 | semidirect |
| 24. C42×D53 | C2×C4 | semidirect |
| 27. C2×C42×C53 | C2×C4 | semidirect |
| 36. C22×C4×C53 | C4⋊C4 | semidirect |
| 38. C22×Dic53 | C4⋊C4 | semidirect |
| 40. C2×C4×D53 | C4⋊C4 | semidirect |
| 46. C42×C53 | C22×C4 | semidirect |
| 47. C4×Dic53 | C22×C4 | semidirect |
| 59. C2×C4×C53 | C2×C4⋊C4 | semidirect |
| 61. C2×Dic53 | C2×C4⋊C4 | semidirect |
| 63. C4×D53 | C2×C4⋊C4 | semidirect |
| 67. C22×C53 | #384 | semidirect |
| 70. C2×D53 | #384 | semidirect |
| 77. C4×C53 | C22×C4⋊C4 | semidirect |
| 78. Dic53 | C22×C4⋊C4 | semidirect |
| 82. C2×C53 | C2×#384 | semidirect |
| 84. D53 | C2×#384 | semidirect |
| 94. C22×C42 | #6157 | semidirect |
| 96. C53 | C22×#384 | semidirect |
| 111. C2×C42 | C2×#6157 | semidirect |
| 127. C22×C4 | C4⋊#6157 | semidirect |
| 131. C42 | C22×#6157 | semidirect |
| 148. C2×C4 | C2×C4⋊#6157 | semidirect |
| 156. C22 | #16811569 | direct (N × H) |
| 161. C4 | C22×C4⋊#6157 | semidirect |
| 165. C2 | C2×#16811569 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×C4⋊#6157 | 2 |
| C2×#16811569 | 2 |
| C22×C42×D53 | 2 |
| C22×#384 | 53 |