Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
472 conjugacy classes of subgroups; only the 91 normal subgroups are shown.
This group has 472 conjugacy classes of subgroups — too many to draw. Only its 91 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. #20283733 | C2 | semidirect |
| 3. #20273147 | C2 | semidirect |
| 4. #20273067 | C2 | semidirect |
| 5. #20272625 | C2 | semidirect |
| 6. #20272605 | C2 | semidirect |
| 7. C53×#1527 | C2 | semidirect |
| 204. #1527 | D53 | semidirect |
| 240. C53 | #9350 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20284205 | 2 |
| #20283733 | 2 |
| #20273147 | 2 |
| #20273067 | 2 |
| #20272625 | 2 |
| #20272605 | 2 |
| C53×#1527 | 2 |
| #9350 | 53 |