Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
930 conjugacy classes of subgroups; only the 191 normal subgroups are shown.
This group has 930 conjugacy classes of subgroups — too many to draw. Only its 191 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×#16810825 | C2 | semidirect |
| 3. #20276133 | C2 | semidirect |
| 5. #20275070 | C2 | semidirect |
| 6. #20274835 | C2 | semidirect |
| 7. #20274722 | C2 | semidirect |
| 8. C53×#2327 | C2 | semidirect |
| 47. C4⋊Q8×C53 | D4 | semidirect |
| 149. #2327 | D53 | semidirect |
| 179. C53 | #28166 | semidirect |
| 189. C4⋊Q8 | D212 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16810825 | 2 |
| #20277440 | 2 |
| #20276133 | 2 |
| #20275802 | 2 |
| #20275070 | 2 |
| #20274835 | 2 |
| #20274722 | 2 |
| C53×#2327 | 2 |
| #28166 | 53 |