Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
150 conjugacy classes of subgroups; only the 75 normal subgroups are shown.
This group has 150 conjugacy classes of subgroups — too many to draw. Only its 75 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 |
|---|---|---|
| 25. C32×C53 | Q8 | semidirect |
| 74. C53 | #13734 | semidirect |
| 85. C32 | Dic106 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20276994 | 2 |
| #20276990 | 2 |
| #20272917 | 2 |
| #20272915 | 2 |
| C53×#1397 | 2 |
| #13734 | 53 |