Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
242 conjugacy classes of subgroups; only the 80 normal subgroups are shown.
This group has 242 conjugacy classes of subgroups — too many to draw. Only its 80 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. #20291101 | C2 | semidirect |
| 2. #20289744 | C2 | semidirect |
| 3. #20289666 | C2 | semidirect |
| 4. C8×#11719910 | C2 | semidirect |
| 48. #11719910 | D8 | semidirect |
| 60. C8×C53 | M32 | semidirect |
| 95. C53 | #12039 | semidirect |
| 144. C8 | #13133292 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20291101 | 2 |
| #20289744 | 2 |
| #20289666 | 2 |
| C8×#11719910 | 2 |
| #20273509 | 2 |
| #12039 | 53 |