Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
1386 conjugacy classes of subgroups; only the 331 normal subgroups are shown.
This group has 1386 conjugacy classes of subgroups — too many to draw. Only its 331 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 |
|---|---|---|
| 1. C2×#16811017 | C2 | semidirect |
| 3. C2×#16811003 | C2 | semidirect |
| 4. #20280825 | C2 | semidirect |
| 5. C53×#1726 | C2 | semidirect |
| 90. #1726 | D53 | semidirect |
| 107. C53 | #33309 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16811017 | 2 |
| C2×#16811007 | 2 |
| C2×#16811003 | 2 |
| #20280825 | 2 |
| C53×#1726 | 2 |
| #33309 | 53 |