Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
272 conjugacy classes of subgroups; only the 75 normal subgroups are shown.
This group has 272 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 |
|---|---|---|
| 3. #20272749 | C2 | semidirect |
| 117. C53 | #11914 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20285374 | 2 |
| #20276320 | 2 |
| #20272749 | 2 |
| C53×#2166 | 2 |
| #11914 | 53 |