Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
914 conjugacy classes of subgroups; only the 159 normal subgroups are shown.
This group has 914 conjugacy classes of subgroups — too many to draw. Only its 159 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. #20276464 | C2 | semidirect |
| 2. #20276443 | C2 | semidirect |
| 3. C2×#16810405 | C2 | semidirect |
| 4. #20274757 | C2 | semidirect |
| 6. C2×#13133157 | C22 | semidirect |
| 7. C2×#13133153 | C22 | semidirect |
| 8. C2×#13133153 | C22 | semidirect |
| 216. C53 | #12740 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20276464 | 2 |
| #20276443 | 2 |
| C2×#16810405 | 2 |
| #20274757 | 2 |
| C2×C53×#575 | 2 |
| #12740 | 53 |