Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
150 conjugacy classes of subgroups; only the 71 normal subgroups are shown.
This group has 150 conjugacy classes of subgroups — too many to draw. Only its 71 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 |
|---|---|---|
| 18. #13133123 | Q8 | semidirect |
| 74. C53 | #13734 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20276990 | 2 |
| #20272916 | 2 |
| #20272914 | 2 |
| #20272849 | 2 |
| C53×#2253 | 2 |
| #13734 | 53 |