Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
434 conjugacy classes of subgroups; only the 120 normal subgroups are shown.
This group has 434 conjugacy classes of subgroups — too many to draw. Only its 120 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 |
|---|---|---|
| 9. #16811542 | C4 | direct (N × H) |
| 138. C4×C53 | #362 | semidirect |
| 173. C53 | C4×#362 | semidirect |
| 292. C4 | #16811542 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16811542 | 2 |
| C4×#13133292 | 2 |
| C4×#13133287 | 2 |
| #20289789 | 2 |
| C4×Q16×D53 | 2 |
| C4×#362 | 53 |