Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
754 conjugacy classes of subgroups; only the 115 normal subgroups are shown.
This group has 754 conjugacy classes of subgroups — too many to draw. Only its 115 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. #20275703 | C2 | semidirect |
| 3. #20275558 | C2 | semidirect |
| 4. #20273307 | C2 | semidirect |
| 5. #20273152 | C2 | semidirect |
| 6. #20273152 | C2 | semidirect |
| 7. C53×#1560 | C2 | semidirect |
| 232. #1560 | D53 | semidirect |
| 269. C53 | #8470 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20288622 | 2 |
| #20275703 | 2 |
| #20275558 | 2 |
| #20273307 | 2 |
| #20273152 | 2 |
| C53×#1560 | 2 |
| #8470 | 53 |