Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
698 conjugacy classes of subgroups; only the 148 normal subgroups are shown.
This group has 698 conjugacy classes of subgroups — too many to draw. Only its 148 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. #20290630 | C2 | semidirect |
| 2. #20290429 | C2 | semidirect |
| 3. C2×D4⋊#88324 | C2 | semidirect |
| 21. C4×#88324 | D4 | semidirect |
| 37. #127×C53 | C8 | semidirect |
| 142. C53 | #9642 | semidirect |
| 149. #127 | #88324 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20290630 | 2 |
| #20290429 | 2 |
| C2×D4⋊#88324 | 2 |
| #127×Dic53 | 2 |
| #9642 | 53 |