Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
584 conjugacy classes of subgroups; only the 105 normal subgroups are shown.
This group has 584 conjugacy classes of subgroups — too many to draw. Only its 105 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. #20284747 | C2 | semidirect |
| 3. #20275655 | C2 | semidirect |
| 4. #20273115 | C2 | semidirect |
| 5. C53×#1275 | C2 | semidirect |
| 70. C2×C8×C53 | SD16 | semidirect |
| 135. #1275 | D53 | semidirect |
| 156. C53 | #10034 | semidirect |
| 212. C2×C8 | #11719913 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20285161 | 2 |
| #20284747 | 2 |
| #20275655 | 2 |
| #20273115 | 2 |
| C53×#1275 | 2 |
| #10034 | 53 |