Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
1102 conjugacy classes of subgroups; only the 351 normal subgroups are shown.
This group has 1102 conjugacy classes of subgroups — too many to draw. Only its 351 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. #20283326 | C2 | semidirect |
| 3. #20276465 | C2 | semidirect |
| 4. C2×#16810440 | C2 | semidirect |
| 5. C53×#3407 | C2 | semidirect |
| 111. #3407 | D53 | semidirect |
| 133. C53 | #33393 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16811440 | 2 |
| #20283326 | 2 |
| #20276465 | 2 |
| C2×#16810440 | 2 |
| C53×#3407 | 2 |
| #33393 | 53 |