Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
402 conjugacy classes of subgroups; only the 109 normal subgroups are shown.
This group has 402 conjugacy classes of subgroups — too many to draw. Only its 109 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. C2×#16810449 | C2 | semidirect |
| 5. #20275500 | C2 | semidirect |
| 6. #20272824 | C2 | semidirect |
| 7. C53×#1379 | C2 | semidirect |
| 19. #16810431 | C4 | semidirect |
| 43. #13133153 | C2×C4 | semidirect |
| 60. C2×C16×C53 | C2×C4 | semidirect |
| 160. #1379 | D53 | semidirect |
| 185. C53 | #12945 | semidirect |
| 210. C2×C16 | C4×D53 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20283592 | 2 |
| C2×#16810449 | 2 |
| C2×#16810431 | 2 |
| #20276428 | 2 |
| #20275500 | 2 |
| #20272824 | 2 |
| C53×#1379 | 2 |
| #12945 | 53 |