Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
480 conjugacy classes of subgroups; only the 103 normal subgroups are shown.
This group has 480 conjugacy classes of subgroups — too many to draw. Only its 103 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. #20283885 | C2 | semidirect |
| 2. #20275556 | C2 | semidirect |
| 3. #20273429 | C2 | semidirect |
| 4. #20273322 | C2 | semidirect |
| 5. #20272625 | C2 | semidirect |
| 6. #20272588 | C2 | semidirect |
| 235. C53 | #9340 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20283885 | 2 |
| #20275556 | 2 |
| #20273429 | 2 |
| #20273322 | 2 |
| #20272625 | 2 |
| #20272588 | 2 |
| C53×#3217 | 2 |
| #9340 | 53 |