Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
354 conjugacy classes of subgroups; only the 188 normal subgroups are shown.
This group has 354 conjugacy classes of subgroups — too many to draw. Only its 188 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 |
|---|---|---|
| 2. #20289627 | C2 | semidirect |
| 3. C8×#11719910 | C2 | semidirect |
| 15. #13133292 | C8 | direct (N × H) |
| 46. #11719910 | C2×C8 | semidirect |
| 59. C8×C53 | M32 | semidirect |
| 61. #88322 | M32 | semidirect |
| 92. C53 | C8×M32 | semidirect |
| 140. C8 | #13133292 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×#13133292 | 2 |
| #20289627 | 2 |
| C8×#11719910 | 2 |
| C82×D53 | 2 |
| C8×M32 | 53 |