Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
446 conjugacy classes of subgroups; only the 91 normal subgroups are shown.
This group has 446 conjugacy classes of subgroups — too many to draw. Only its 91 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. #20272734 | C2 | semidirect |
| 5. #20272733 | C2 | semidirect |
| 6. #20272732 | C2 | semidirect |
| 7. C53×#1350 | C2 | semidirect |
| 178. #1350 | D53 | direct (N × H) |
| 184. D53 | #1350 | direct (N × H) |
| 204. C53 | C2×#1350 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #467×D53 | 2 |
| C22⋊C16×D53 | 2 |
| #341×D53 | 2 |
| #20272734 | 2 |
| #20272733 | 2 |
| #20272732 | 2 |
| C53×#1350 | 2 |
| C2×#1350 | 53 |