Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
206 conjugacy classes of subgroups; only the 91 normal subgroups are shown.
This group has 206 conjugacy classes of subgroups — too many to draw. Only its 91 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 |
|---|---|---|
| 3. #20272915 | C2 | semidirect |
| 4. #20272914 | C2 | semidirect |
| 5. C53×#1423 | C2 | semidirect |
| 9. C32×D53 | C4 | semidirect |
| 21. #13133123 | C2×C4 | semidirect |
| 24. C32×C53 | C2×C4 | semidirect |
| 62. #1423 | D53 | direct (N × H) |
| 66. D53 | #1423 | direct (N × H) |
| 75. C53 | C2×#1423 | semidirect |
| 86. C32 | C4×D53 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C32×D53 | 2 |
| #366×D53 | 2 |
| #20272915 | 2 |
| #20272914 | 2 |
| C53×#1423 | 2 |
| C2×#1423 | 53 |