Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
770 conjugacy classes of subgroups; only the 255 normal subgroups are shown.
This group has 770 conjugacy classes of subgroups — too many to draw. Only its 255 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 |
|---|---|---|
| 3. #20274889 | C2 | semidirect |
| 4. #20274856 | C2 | semidirect |
| 6. #20274620 | C2 | semidirect |
| 7. C53×#1838 | C2 | semidirect |
| 108. #1838 | D53 | semidirect |
| 130. C53 | #20830 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20283347 | 2 |
| C2×#97×D53 | 2 |
| #20274889 | 2 |
| #20274856 | 2 |
| #20274752 | 2 |
| #20274620 | 2 |
| C53×#1838 | 2 |
| #20830 | 53 |