Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
720 conjugacy classes of subgroups; only the 138 normal subgroups are shown.
This group has 720 conjugacy classes of subgroups — too many to draw. Only its 138 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. #20290501 | C2 | semidirect |
| 2. C4×#13133284 | C2 | semidirect |
| 3. C2×D4⋊#88324 | C2 | semidirect |
| 25. C4⋊#88324 | D4 | semidirect |
| 191. C53 | #9678 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20290501 | 2 |
| C4×#13133284 | 2 |
| C2×D4⋊#88324 | 2 |
| #127×Dic53 | 2 |
| #9678 | 53 |