Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
260 conjugacy classes of subgroups; only the 79 normal subgroups are shown.
This group has 260 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. #20276995 | C2 | semidirect |
| 2. #20276988 | C2 | semidirect |
| 6. #20272633 | C2 | semidirect |
| 7. C53×#1710 | C2 | semidirect |
| 100. #1710 | D53 | semidirect |
| 122. C53 | #12536 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20276995 | 2 |
| #20276988 | 2 |
| #20276940 | 2 |
| #20274307 | 2 |
| #20272633 | 2 |
| C53×#1710 | 2 |
| #12536 | 53 |