Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
470 conjugacy classes of subgroups; only the 93 normal subgroups are shown.
This group has 470 conjugacy classes of subgroups — too many to draw. Only its 93 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. #20283369 | C2 | semidirect |
| 3. #20274811 | C2 | semidirect |
| 6. #20272620 | C2 | semidirect |
| 7. C53×#1298 | C2 | semidirect |
| 17. #16810665 | C4 | semidirect |
| 18. #16810665 | C4 | semidirect |
| 20. #16810629 | C4 | semidirect |
| 21. #16810629 | C4 | semidirect |
| 221. #1298 | D53 | semidirect |
| 255. C53 | #9348 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20284656 | 2 |
| #20283369 | 2 |
| #20274811 | 2 |
| #20273284 | 2 |
| #20273074 | 2 |
| #20272620 | 2 |
| C53×#1298 | 2 |
| #9348 | 53 |