Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
364 conjugacy classes of subgroups; only the 75 normal subgroups are shown.
This group has 364 conjugacy classes of subgroups — too many to draw. Only its 75 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. #20274890 | C2 | semidirect |
| 3. #20273445 | C2 | semidirect |
| 6. #20272625 | C2 | semidirect |
| 7. C53×#1531 | C2 | semidirect |
| 154. #1531 | D53 | semidirect |
| 181. C53 | #10526 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20286098 | 2 |
| #20274890 | 2 |
| #20273445 | 2 |
| #20273438 | 2 |
| #20273325 | 2 |
| #20272625 | 2 |
| C53×#1531 | 2 |
| #10526 | 53 |