Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
558 conjugacy classes of subgroups; only the 109 normal subgroups are shown.
This group has 558 conjugacy classes of subgroups — too many to draw. Only its 109 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. #20283434 | C2 | semidirect |
| 3. #20275539 | C2 | semidirect |
| 4. #20273382 | C2 | semidirect |
| 5. #20273276 | C2 | semidirect |
| 6. #20272574 | C2 | semidirect |
| 7. C53×#1275 | C2 | semidirect |
| 11. #16811000 | C4 | semidirect |
| 12. #16810970 | C4 | semidirect |
| 102. C2×C8×C53 | D8 | semidirect |
| 195. #1275 | D53 | semidirect |
| 222. C53 | #9293 | semidirect |
| 304. C2×C8 | D424 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20285635 | 2 |
| #20283434 | 2 |
| #20275539 | 2 |
| #20273382 | 2 |
| #20273276 | 2 |
| #20272574 | 2 |
| C53×#1275 | 2 |
| #9293 | 53 |