Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
442 conjugacy classes of subgroups; only the 131 normal subgroups are shown.
This group has 442 conjugacy classes of subgroups — too many to draw. Only its 131 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×#16810444 | C2 | semidirect |
| 2. #20272756 | C2 | direct (N × H) |
| 6. #16810444 | C22 | semidirect |
| 114. C2×C53 | #1359 | semidirect |
| 126. C53 | C2×#1359 | semidirect |
| 223. C2 | #20272756 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16810444 | 2 |
| #20272756 | 2 |
| C2×C53×#492 | 2 |
| C2×#1359 | 53 |