Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
222 conjugacy classes of subgroups; only the 136 normal subgroups are shown.
This group has 222 conjugacy classes of subgroups — too many to draw. Only its 136 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. #20289827 | C2 | direct (N × H) |
| 4. #16811555 | C4 | semidirect |
| 6. C2×#13133267 | C4 | semidirect |
| 12. #13133267 | C2×C4 | semidirect |
| 70. C2×C53 | #1398 | semidirect |
| 80. C53 | C2×#1398 | semidirect |
| 135. C2 | #20289827 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16811555 | 2 |
| #20289827 | 2 |
| C2×#16810398 | 2 |
| C2×#1398 | 53 |