Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
814 conjugacy classes of subgroups; only the 219 normal subgroups are shown.
This group has 814 conjugacy classes of subgroups — too many to draw. Only its 219 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. #20285275 | C2 | semidirect |
| 3. #20274317 | C2 | semidirect |
| 4. #20274313 | C2 | semidirect |
| 5. #20274308 | C2 | semidirect |
| 6. #20274303 | C2 | semidirect |
| 7. C2×C8×#88322 | C2 | semidirect |
| 8. C53×#3160 | C2 | semidirect |
| 70. C2×C8×C53 | SD16 | semidirect |
| 109. #88322 | #135 | semidirect |
| 123. #3160 | D53 | semidirect |
| 156. C53 | #19596 | semidirect |
| 203. C2×C8 | #11719924 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20285275 | 2 |
| #20285143 | 2 |
| #20274317 | 2 |
| #20274313 | 2 |
| #20274308 | 2 |
| #20274303 | 2 |
| C2×C8×#88322 | 2 |
| C53×#3160 | 2 |
| #19596 | 53 |