Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
350 conjugacy classes of subgroups; only the 111 normal subgroups are shown.
This group has 350 conjugacy classes of subgroups — too many to draw. Only its 111 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. #20272774 | C2 | semidirect |
| 5. #20272773 | C2 | semidirect |
| 6. #20272772 | C2 | semidirect |
| 7. C53×#1365 | C2 | semidirect |
| 129. #1365 | D53 | direct (N × H) |
| 133. D53 | #1365 | direct (N × H) |
| 151. C53 | C2×#1365 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #500×D53 | 2 |
| C4⋊C16×D53 | 2 |
| #335×D53 | 2 |
| #20272774 | 2 |
| #20272773 | 2 |
| #20272772 | 2 |
| C53×#1365 | 2 |
| C2×#1365 | 53 |