Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
414 conjugacy classes of subgroups; only the 175 normal subgroups are shown.
This group has 414 conjugacy classes of subgroups — too many to draw. Only its 175 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 |
|---|---|---|
| 11. #16810375 | C4 | semidirect |
| 12. #16810373 | C4 | semidirect |
| 24. C4×#88322 | C8 | semidirect |
| 102. C53 | #8266 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C42×#88322 | 2 |
| #20273461 | 2 |
| #20272999 | 2 |
| #20272548 | 2 |
| C53×#1276 | 2 |
| #8266 | 53 |