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 |
|---|---|---|
| 3. #20272750 | C2 | semidirect |
| 4. #20272749 | C2 | semidirect |
| 5. C53×#1356 | C2 | semidirect |
| 109. #1356 | D53 | direct (N × H) |
| 113. D53 | #1356 | direct (N × H) |
| 127. C53 | C2×#1356 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #491×D53 | 2 |
| #347×D53 | 2 |
| #20272750 | 2 |
| #20272749 | 2 |
| C53×#1356 | 2 |
| C2×#1356 | 53 |