Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
260 conjugacy classes of subgroups; only the 75 normal subgroups are shown.
This group has 260 conjugacy classes of subgroups — too many to draw. Only its 75 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. #20276988 | C2 | semidirect |
| 4. #20274324 | C2 | semidirect |
| 6. #20272634 | C2 | semidirect |
| 7. C53×#2254 | C2 | semidirect |
| 96. #2254 | 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 |
|---|---|
| #20276988 | 2 |
| #20276940 | 2 |
| #20276939 | 2 |
| #20274324 | 2 |
| #20274308 | 2 |
| #20272634 | 2 |
| C53×#2254 | 2 |
| #12536 | 53 |