Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
2398 conjugacy classes of subgroups; only the 1067 normal subgroups are shown.
This group has 2398 conjugacy classes of subgroups — too many to draw. Only its 1067 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×#16811021 | C2 | direct (N × H) |
| 10. #16811021 | C22 | direct (N × H) |
| 26. C22×C8×C53 | Q8 | semidirect |
| 41. C2×C8×C53 | C2×Q8 | semidirect |
| 60. C8×C53 | C22×Q8 | semidirect |
| 62. C22×C53 | #498 | semidirect |
| 74. C2×C53 | C2×#498 | semidirect |
| 87. C53 | C22×#498 | semidirect |
| 93. C22×C8 | Dic106 | semidirect |
| 114. C2×C8 | C2×Dic106 | semidirect |
| 133. C8 | C22×Dic106 | semidirect |
| 134. C22 | #16811021 | direct (N × H) |
| 142. C2 | C2×#16811021 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#13133217 | 2 |
| C2×#16811021 | 2 |
| C22×#13133149 | 2 |
| C22×C4×C8×C53 | 2 |
| C22×#498 | 53 |