Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
314 conjugacy classes of subgroups; only the 71 normal subgroups are shown.
This group has 314 conjugacy classes of subgroups — too many to draw. Only its 71 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. #20287108 | C2 | semidirect |
| 2. #20276939 | C2 | semidirect |
| 3. #20276756 | C2 | semidirect |
| 5. #20272772 | C2 | semidirect |
| 6. #20272680 | C2 | semidirect |
| 7. C53×D4⋊C16 | C2 | semidirect |
| 89. D4×C53 | SD32 | semidirect |
| 136. D4⋊C16 | D53 | semidirect |
| 159. C53 | #12342 | semidirect |
| 232. D4 | #13133162 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20287108 | 2 |
| #20276939 | 2 |
| #20276756 | 2 |
| #20274070 | 2 |
| #20272772 | 2 |
| #20272680 | 2 |
| C53×D4⋊C16 | 2 |
| #12342 | 53 |