Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
478 conjugacy classes of subgroups; only the 93 normal subgroups are shown.
This group has 478 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. #20274815 | C2 | semidirect |
| 6. #20272592 | C2 | semidirect |
| 7. C53×#1282 | C2 | semidirect |
| 17. C2×#13133151 | C4 | semidirect |
| 18. C2×#13133149 | C4 | semidirect |
| 20. C2×#13133139 | C4 | semidirect |
| 21. C2×#13133139 | C4 | semidirect |
| 222. #1282 | D53 | semidirect |
| 256. C53 | #9242 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16810948 | 2 |
| #20283369 | 2 |
| #20274815 | 2 |
| #20273230 | 2 |
| #20273074 | 2 |
| #20272592 | 2 |
| C53×#1282 | 2 |
| #9242 | 53 |