Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
380 conjugacy classes of subgroups; only the 103 normal subgroups are shown.
This group has 380 conjugacy classes of subgroups — too many to draw. Only its 103 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 |
|---|---|---|
| 4. #20275503 | C2 | semidirect |
| 5. #20272826 | C2 | semidirect |
| 6. #20272803 | C2 | semidirect |
| 7. C2×C53×#368 | C2 | semidirect |
| 17. #16810431 | C4 | semidirect |
| 137. C2×#368 | D53 | semidirect |
| 164. C53 | #12947 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20283631 | 2 |
| #20276442 | 2 |
| C2×#16810431 | 2 |
| #20275503 | 2 |
| #20272826 | 2 |
| #20272803 | 2 |
| C2×C53×#368 | 2 |
| #12947 | 53 |