Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
466 conjugacy classes of subgroups; only the 120 normal subgroups are shown.
This group has 466 conjugacy classes of subgroups — too many to draw. Only its 120 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. C4×#13133292 | C2 | semidirect |
| 3. C4×#13133285 | C2 | semidirect |
| 4. #20289786 | C2 | semidirect |
| 9. #16811540 | C4 | direct (N × H) |
| 15. Q16×Dic53 | C4 | semidirect |
| 18. C4×D424 | C4 | semidirect |
| 19. #16810705 | C4 | semidirect |
| 23. C4×Q16×C53 | C4 | semidirect |
| 27. #13133292 | C2×C4 | semidirect |
| 30. #13133285 | C2×C4 | semidirect |
| 77. Q16×C53 | C42 | semidirect |
| 98. D424 | C42 | semidirect |
| 146. C4×C53 | #360 | semidirect |
| 167. C4×Q16 | #6157 | semidirect |
| 181. C53 | C4×#360 | semidirect |
| 232. Q16 | C4×#6157 | semidirect |
| 307. C4 | #16811540 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16811540 | 2 |
| C4×#13133292 | 2 |
| C4×#13133285 | 2 |
| #20289786 | 2 |
| C4×#13133240 | 2 |
| C4×#360 | 53 |