Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
398 conjugacy classes of subgroups; only the 103 normal subgroups are shown.
This group has 398 conjugacy classes of subgroups — too many to draw. Only its 103 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. #20276964 | C2 | semidirect |
| 2. #20274330 | C2 | semidirect |
| 3. C8×#11719908 | C2 | semidirect |
| 4. C53×#1712 | C2 | semidirect |
| 33. #11719908 | D8 | semidirect |
| 42. C8×C53 | D16 | semidirect |
| 54. #1712 | D53 | semidirect |
| 67. C53 | #12515 | semidirect |
| 98. C8 | #13133158 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20276964 | 2 |
| #20274330 | 2 |
| C8×#11719908 | 2 |
| C53×#1712 | 2 |
| #12515 | 53 |