Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
906 conjugacy classes of subgroups; only the 211 normal subgroups are shown.
This group has 906 conjugacy classes of subgroups — too many to draw. Only its 211 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. #20285290 | C2 | semidirect |
| 2. #20285143 | C2 | semidirect |
| 3. #20274387 | C2 | semidirect |
| 4. #20274384 | C2 | semidirect |
| 5. #20274382 | C2 | semidirect |
| 6. #20274379 | C2 | semidirect |
| 7. C2×#16810344 | C2 | semidirect |
| 8. C53×#3147 | C2 | semidirect |
| 80. C2×C8×C53 | D8 | semidirect |
| 136. #3147 | D53 | semidirect |
| 169. C53 | #19616 | semidirect |
| 225. C2×C8 | #11719922 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20285290 | 2 |
| #20285143 | 2 |
| #20274387 | 2 |
| #20274384 | 2 |
| #20274382 | 2 |
| #20274379 | 2 |
| C2×#16810344 | 2 |
| C53×#3147 | 2 |
| #19616 | 53 |