Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
972 conjugacy classes of subgroups; only the 147 normal subgroups are shown.
This group has 972 conjugacy classes of subgroups — too many to draw. Only its 147 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. C2×#16810349 | C2 | semidirect |
| 4. #20272593 | C2 | semidirect |
| 5. C53×#2316 | C2 | semidirect |
| 12. #16810540 | C4 | semidirect |
| 156. C2×C4×C53 | #102 | semidirect |
| 204. #2316 | D53 | semidirect |
| 232. C53 | #9019 | semidirect |
| 377. C2×C4 | #13133137 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16810540 | 2 |
| #20274645 | 2 |
| C2×#16810349 | 2 |
| #20272593 | 2 |
| C53×#2316 | 2 |
| #9019 | 53 |