Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
386 conjugacy classes of subgroups; only the 101 normal subgroups are shown.
This group has 386 conjugacy classes of subgroups — too many to draw. Only its 101 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 |
|---|---|---|
| 2. C4×#13133152 | C2 | semidirect |
| 3. #20273470 | C2 | semidirect |
| 6. #20272606 | C2 | semidirect |
| 7. C53×#1299 | C2 | semidirect |
| 176. #1299 | D53 | semidirect |
| 205. C53 | #8672 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20283676 | 2 |
| C4×#13133152 | 2 |
| #20273470 | 2 |
| #20273155 | 2 |
| #20273152 | 2 |
| #20272606 | 2 |
| C53×#1299 | 2 |
| #8672 | 53 |