Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
294 conjugacy classes of subgroups; only the 65 normal subgroups are shown.
This group has 294 conjugacy classes of subgroups — too many to draw. Only its 65 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. #20287684 | C2 | semidirect |
| 5. #20272766 | C2 | semidirect |
| 6. #20272686 | C2 | semidirect |
| 7. C53×#1338 | C2 | semidirect |
| 91. Dic212 | SD16 | semidirect |
| 141. #1338 | D53 | semidirect |
| 166. C53 | #12361 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20287684 | 2 |
| #20276957 | 2 |
| #20276756 | 2 |
| #20274199 | 2 |
| #20272766 | 2 |
| #20272686 | 2 |
| C53×#1338 | 2 |
| #12361 | 53 |