Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
402 conjugacy classes of subgroups; only the 75 normal subgroups are shown.
This group has 402 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. #20275564 | C2 | semidirect |
| 3. #20273482 | C2 | semidirect |
| 4. #20273437 | C2 | semidirect |
| 5. #20273312 | C2 | semidirect |
| 6. #20272587 | C2 | semidirect |
| 7. C53×#1525 | C2 | semidirect |
| 188. #1525 | D53 | semidirect |
| 219. C53 | #10496 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20285698 | 2 |
| #20275564 | 2 |
| #20273482 | 2 |
| #20273437 | 2 |
| #20273312 | 2 |
| #20272587 | 2 |
| C53×#1525 | 2 |
| #10496 | 53 |