Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
1502 conjugacy classes of subgroups; only the 331 normal subgroups are shown.
This group has 1502 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 |
| 2. C2×#16811012 | C2 | semidirect |
| 3. C2×#16811007 | C2 | semidirect |
| 4. #20283072 | C2 | semidirect |
| 5. C4×#97×C53 | C2 | semidirect |
| 42. #97×C53 | D4 | semidirect |
| 43. C4×C8×C53 | D4 | semidirect |
| 106. C4×#97 | D53 | semidirect |
| 125. C53 | #33306 | semidirect |
| 148. #97 | D212 | semidirect |
| 149. C4×C8 | D212 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16811017 | 2 |
| C2×#16811012 | 2 |
| C2×#16811007 | 2 |
| #20283072 | 2 |
| C4×#97×C53 | 2 |
| #33306 | 53 |