Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
446 conjugacy classes of subgroups; only the 87 normal subgroups are shown.
This group has 446 conjugacy classes of subgroups — too many to draw. Only its 87 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 |
|---|---|---|
| 1. #20276043 | C2 | semidirect |
| 2. #20275961 | C2 | semidirect |
| 4. #20272538 | C2 | semidirect |
| 5. #20272538 | C2 | semidirect |
| 225. C53 | #7765 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20276043 | 2 |
| #20275961 | 2 |
| #20275851 | 2 |
| #20272538 | 2 |
| #20272536 | 2 |
| C53×#2727 | 2 |
| #7765 | 53 |