Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
930 conjugacy classes of subgroups; only the 187 normal subgroups are shown.
This group has 930 conjugacy classes of subgroups — too many to draw. Only its 187 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×#16810828 | C2 | semidirect |
| 2. #20277434 | C2 | semidirect |
| 3. #20276134 | C2 | semidirect |
| 5. #20275073 | C2 | semidirect |
| 6. #20274835 | C2 | semidirect |
| 7. #20274725 | C2 | semidirect |
| 34. #13133217 | D4 | semidirect |
| 179. C53 | #28166 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16810828 | 2 |
| #20277434 | 2 |
| #20276134 | 2 |
| #20275803 | 2 |
| #20275073 | 2 |
| #20274835 | 2 |
| #20274725 | 2 |
| C53×#2328 | 2 |
| #28166 | 53 |