Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
814 conjugacy classes of subgroups; only the 179 normal subgroups are shown.
This group has 814 conjugacy classes of subgroups — too many to draw. Only its 179 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. C2×#16811062 | C2 | semidirect |
| 3. #494×D53 | C2 | semidirect |
| 4. #20276985 | C2 | semidirect |
| 5. #20276970 | C2 | semidirect |
| 6. #20276968 | C2 | semidirect |
| 7. #20276967 | C2 | semidirect |
| 8. C4×#13133156 | C2 | semidirect |
| 9. C53×#2248 | C2 | semidirect |
| 64. #13133156 | D4 | semidirect |
| 157. C4×C53 | #510 | semidirect |
| 169. #2248 | D53 | semidirect |
| 203. C53 | #33718 | semidirect |
| 328. C4 | #16811062 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16811062 | 2 |
| #20285142 | 2 |
| #494×D53 | 2 |
| #20276985 | 2 |
| #20276970 | 2 |
| #20276968 | 2 |
| #20276967 | 2 |
| C4×#13133156 | 2 |
| C53×#2248 | 2 |
| #33718 | 53 |