Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
540 conjugacy classes of subgroups; only the 162 normal subgroups are shown.
This group has 540 conjugacy classes of subgroups — too many to draw. Only its 162 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 |
|---|---|---|
| 8. #16811483 | C4 | direct (N × H) |
| 120. C4×C53 | #333 | semidirect |
| 148. C53 | C4×#333 | semidirect |
| 255. C4 | #16811483 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×#13133284 | 2 |
| C2×#16811483 | 2 |
| #20289593 | 2 |
| C4×#13133215 | 2 |
| C4×#333 | 53 |