Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
544 conjugacy classes of subgroups; only the 79 normal subgroups are shown.
This group has 544 conjugacy classes of subgroups — too many to draw. Only its 79 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. #20285909 | C2 | semidirect |
| 2. #20285720 | C2 | semidirect |
| 4. #20273135 | C2 | semidirect |
| 5. #20273066 | C2 | semidirect |
| 6. #20272586 | C2 | semidirect |
| 7. C53×#1496 | C2 | semidirect |
| 199. #1496 | D53 | semidirect |
| 234. C53 | #10121 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20285909 | 2 |
| #20285720 | 2 |
| #20285183 | 2 |
| #20273135 | 2 |
| #20273066 | 2 |
| #20272586 | 2 |
| C53×#1496 | 2 |
| #10121 | 53 |