Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
934 conjugacy classes of subgroups; only the 159 normal subgroups are shown.
This group has 934 conjugacy classes of subgroups — too many to draw. Only its 159 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×#16811000 | C2 | semidirect |
| 2. C2×#16810999 | C2 | semidirect |
| 3. #20275520 | C2 | semidirect |
| 4. #20272542 | C2 | semidirect |
| 5. C53×#1957 | C2 | semidirect |
| 73. C2×C8×C53 | D8 | semidirect |
| 82. C2×#88322 | D8 | semidirect |
| 145. #1957 | D53 | semidirect |
| 166. C53 | #10304 | semidirect |
| 227. C2×C8 | #11719922 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16811000 | 2 |
| C2×#16810999 | 2 |
| #20275520 | 2 |
| #20272542 | 2 |
| C53×#1957 | 2 |
| #10304 | 53 |