Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
372 conjugacy classes of subgroups; only the 111 normal subgroups are shown.
This group has 372 conjugacy classes of subgroups — too many to draw. Only its 111 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. #20273461 | C2 | semidirect |
| 3. C2×#16810375 | C2 | semidirect |
| 6. #20272566 | C2 | semidirect |
| 7. C53×#1283 | C2 | semidirect |
| 155. #1283 | D53 | semidirect |
| 181. C53 | #8606 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20283360 | 2 |
| #20273461 | 2 |
| C2×#16810375 | 2 |
| #20273103 | 2 |
| #20273100 | 2 |
| #20272566 | 2 |
| C53×#1283 | 2 |
| #8606 | 53 |