Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
822 conjugacy classes of subgroups; only the 331 normal subgroups are shown.
This group has 822 conjugacy classes of subgroups — too many to draw. Only its 331 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 |
|---|---|---|
| 41. #97×C53 | Q8 | semidirect |
| 42. C4×C8×C53 | Q8 | semidirect |
| 116. C53 | #33317 | semidirect |
| 132. #97 | Dic106 | semidirect |
| 134. C4×C8 | Dic106 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16811032 | 2 |
| #20283093 | 2 |
| #20283078 | 2 |
| #20274883 | 2 |
| #20274879 | 2 |
| C4×#97×C53 | 2 |
| #33317 | 53 |