Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
826 conjugacy classes of subgroups; only the 219 normal subgroups are shown.
This group has 826 conjugacy classes of subgroups — too many to draw. Only its 219 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×#16811055 | C2 | semidirect |
| 2. #20285143 | C2 | semidirect |
| 3. #20276986 | C2 | semidirect |
| 4. #20276981 | C2 | semidirect |
| 5. C2×C53×#346 | C2 | semidirect |
| 41. C2×C16×C53 | D4 | semidirect |
| 104. C2×#346 | D53 | semidirect |
| 124. C53 | #33716 | semidirect |
| 145. C2×C16 | D212 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16811055 | 2 |
| #20285143 | 2 |
| #20276986 | 2 |
| #20276981 | 2 |
| C2×C53×#346 | 2 |
| #33716 | 53 |