Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
286 conjugacy classes of subgroups; only the 80 normal subgroups are shown.
This group has 286 conjugacy classes of subgroups — too many to draw. Only its 80 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 |
|---|---|---|
| 3. #20289871 | C2 | direct (N × H) |
| 110. C2×C53 | #1420 | semidirect |
| 129. C53 | C2×#1420 | semidirect |
| 217. C2 | #20289871 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16811556 | 2 |
| C2×#16811552 | 2 |
| #20289871 | 2 |
| C2×Q32×D53 | 2 |
| C2×#1420 | 53 |