Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
912 conjugacy classes of subgroups; only the 208 normal subgroups are shown.
This group has 912 conjugacy classes of subgroups — too many to draw. Only its 208 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. #20291614 | C2 | semidirect |
| 2. #20289998 | C2 | semidirect |
| 3. #20289986 | C2 | semidirect |
| 4. #20289976 | C2 | semidirect |
| 5. #20289968 | C2 | semidirect |
| 199. C53 | #17409 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20291614 | 2 |
| #20289998 | 2 |
| #20289986 | 2 |
| #20289976 | 2 |
| #20289968 | 2 |
| C2×#16811247 | 2 |
| #17409 | 53 |