Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
492 conjugacy classes of subgroups; only the 81 normal subgroups are shown.
This group has 492 conjugacy classes of subgroups — too many to draw. Only its 81 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 |
|---|---|---|
| 1. #20285728 | C2 | semidirect |
| 3. #20285102 | C2 | semidirect |
| 4. #20273187 | C2 | semidirect |
| 5. #20273133 | C2 | semidirect |
| 6. #20273068 | C2 | semidirect |
| 7. C53×#1291 | C2 | semidirect |
| 196. #1291 | D53 | semidirect |
| 228. C53 | #10124 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20285728 | 2 |
| #20285704 | 2 |
| #20285102 | 2 |
| #20273187 | 2 |
| #20273133 | 2 |
| #20273068 | 2 |
| C53×#1291 | 2 |
| #10124 | 53 |