Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
370 conjugacy classes of subgroups; only the 93 normal subgroups are shown.
This group has 370 conjugacy classes of subgroups — too many to draw. Only its 93 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. C2×#16811023 | C2 | semidirect |
| 5. #20272815 | C2 | semidirect |
| 6. #20272796 | C2 | semidirect |
| 7. C53×#1383 | C2 | semidirect |
| 147. #1383 | D53 | semidirect |
| 169. C53 | #13372 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16811023 | 2 |
| C2×#16810434 | 2 |
| C2×#16810432 | 2 |
| #20275601 | 2 |
| #20272815 | 2 |
| #20272796 | 2 |
| C53×#1383 | 2 |
| #13372 | 53 |