Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
354 conjugacy classes of subgroups; only the 180 normal subgroups are shown.
This group has 354 conjugacy classes of subgroups — too many to draw. Only its 180 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 |
|---|---|---|
| 3. #20289626 | C2 | semidirect |
| 4. C16×#88324 | C2 | semidirect |
| 19. #13133292 | C8 | semidirect |
| 27. #13133156 | C8 | semidirect |
| 48. #11719910 | C2×C8 | semidirect |
| 49. C16×C53 | C2×C8 | semidirect |
| 50. #11719908 | C2×C8 | semidirect |
| 60. #88324 | M32 | semidirect |
| 94. C53 | C8×M32 | semidirect |
| 127. C16 | D53⋊C8 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20290922 | 2 |
| C8×D53⋊C8 | 2 |
| #20289626 | 2 |
| C16×#88324 | 2 |
| #20276308 | 2 |
| C8×M32 | 53 |