Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
822 conjugacy classes of subgroups; only the 151 normal subgroups are shown.
This group has 822 conjugacy classes of subgroups — too many to draw. Only its 151 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. #20272842 | C2 | semidirect |
| 4. #20272841 | C2 | semidirect |
| 5. C53×#1394 | C2 | semidirect |
| 11. #16810606 | C4 | semidirect |
| 48. #13133136 | C2×C4 | semidirect |
| 56. #101×C53 | C2×C4 | semidirect |
| 198. #1394 | D53 | semidirect |
| 221. C53 | #12585 | semidirect |
| 255. #101 | C4×D53 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16810606 | 2 |
| #20277204 | 2 |
| #20272842 | 2 |
| #20272841 | 2 |
| C53×#1394 | 2 |
| #12585 | 53 |