Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
314 conjugacy classes of subgroups; only the 75 normal subgroups are shown.
This group has 314 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 |
|---|---|---|
| 1. #20276940 | C2 | semidirect |
| 2. #20276755 | C2 | semidirect |
| 4. #20272773 | C2 | semidirect |
| 5. #20272679 | C2 | semidirect |
| 6. D4⋊#11719908 | C2 | semidirect |
| 7. C53×#3338 | C2 | semidirect |
| 92. D4×C53 | SD32 | semidirect |
| 130. #3338 | D53 | semidirect |
| 159. C53 | #12342 | semidirect |
| 232. D4 | #13133160 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20276940 | 2 |
| #20276755 | 2 |
| #20274070 | 2 |
| #20272773 | 2 |
| #20272679 | 2 |
| D4⋊#11719908 | 2 |
| C53×#3338 | 2 |
| #12342 | 53 |