Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
830 conjugacy classes of subgroups; only the 207 normal subgroups are shown.
This group has 830 conjugacy classes of subgroups — too many to draw. Only its 207 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. #20272597 | C2 | semidirect |
| 4. #20272596 | C2 | semidirect |
| 5. C53×#1295 | C2 | semidirect |
| 12. #97×D53 | C4 | semidirect |
| 34. #13133128 | C2×C4 | semidirect |
| 42. #97×C53 | C2×C4 | semidirect |
| 124. #1295 | D53 | direct (N × H) |
| 129. D53 | #1295 | direct (N × H) |
| 143. C53 | C2×#1295 | semidirect |
| 165. #97 | C4×D53 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#97×D53 | 2 |
| #382×D53 | 2 |
| #20272597 | 2 |
| #20272596 | 2 |
| C53×#1295 | 2 |
| C2×#1295 | 53 |