Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
3678 conjugacy classes of subgroups; only the 1168 normal subgroups are shown.
This group has 3678 conjugacy classes of subgroups — too many to draw. Only its 1168 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. C2×#16811568 | C2 | direct (N × H) |
| 5. #16811568 | C22 | direct (N × H) |
| 8. C22×C4×Dic53 | C4 | semidirect |
| 9. C2×C42×D53 | C4 | semidirect |
| 11. C22×C42×C53 | C4 | semidirect |
| 20. C2×C4×Dic53 | C2×C4 | semidirect |
| 21. C42×D53 | C2×C4 | semidirect |
| 24. C2×C42×C53 | C2×C4 | semidirect |
| 40. C42×C53 | C22×C4 | semidirect |
| 41. C4×Dic53 | C22×C4 | semidirect |
| 58. C22×C53 | #383 | semidirect |
| 61. C2×D53 | #383 | semidirect |
| 71. C2×C53 | C2×#383 | semidirect |
| 73. D53 | C2×#383 | semidirect |
| 80. C22×C42 | #6157 | semidirect |
| 83. C53 | C22×#383 | semidirect |
| 95. C2×C42 | C2×#6157 | semidirect |
| 113. C42 | C22×#6157 | semidirect |
| 133. C22 | #16811568 | direct (N × H) |
| 141. C2 | C2×#16811568 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16811568 | 2 |
| C22×(C2×#6157)⋊C4 | 2 |
| C22×C42×D53 | 2 |
| C22×#383 | 53 |