Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
1618 conjugacy classes of subgroups; only the 331 normal subgroups are shown.
This group has 1618 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×#16811012 | C2 | semidirect |
| 2. C2×#16811007 | C2 | semidirect |
| 3. C2×#16811000 | C2 | semidirect |
| 4. #20280821 | C2 | semidirect |
| 5. C53×#1726 | C2 | semidirect |
| 37. #97×C53 | D4 | semidirect |
| 38. C4×C8×C53 | D4 | semidirect |
| 93. #1726 | D53 | semidirect |
| 110. C53 | #33308 | semidirect |
| 129. #97 | D212 | semidirect |
| 130. C4×C8 | D212 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16811012 | 2 |
| C2×#16811007 | 2 |
| C2×#16811000 | 2 |
| #20280821 | 2 |
| C53×#1726 | 2 |
| #33308 | 53 |