Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
194 conjugacy classes of subgroups; only the 67 normal subgroups are shown.
This group has 194 conjugacy classes of subgroups — too many to draw. Only its 67 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 |
|---|---|---|
| 62. #11719908 | Q16 | semidirect |
| 117. C53 | #12462 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20276995 | 2 |
| #20276624 | 2 |
| #20274109 | 2 |
| #20272786 | 2 |
| #20272773 | 2 |
| #20272771 | 2 |
| C53×#1676 | 2 |
| #12462 | 53 |