Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
406 conjugacy classes of subgroups; only the 115 normal subgroups are shown.
This group has 406 conjugacy classes of subgroups — too many to draw. Only its 115 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 |
|---|---|---|
| 2. #20276474 | C2 | semidirect |
| 3. C2×#16810408 | C2 | semidirect |
| 4. #20276335 | C2 | semidirect |
| 5. C53×#2110 | C2 | semidirect |
| 112. #2110 | D53 | semidirect |
| 131. C53 | #13199 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20283619 | 2 |
| #20276474 | 2 |
| C2×#16810408 | 2 |
| #20276335 | 2 |
| C53×#2110 | 2 |
| #13199 | 53 |