Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
1342 conjugacy classes of subgroups; only the 239 normal subgroups are shown.
This group has 1342 conjugacy classes of subgroups — too many to draw. Only its 239 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. #493×D53 | C2 | semidirect |
| 2. #20274330 | C2 | semidirect |
| 3. #20274329 | C2 | semidirect |
| 4. C82×D53 | C2 | semidirect |
| 5. C53×#1712 | C2 | semidirect |
| 8. #16811000 | C22 | semidirect |
| 9. #16810999 | C22 | semidirect |
| 12. C8×#88322 | C22 | semidirect |
| 13. C53×#493 | C22 | semidirect |
| 14. C82×C53 | C22 | semidirect |
| 41. C8×D53 | D8 | semidirect |
| 52. C8×C53 | C2×D8 | semidirect |
| 53. #88322 | C2×D8 | semidirect |
| 65. #1712 | D53 | direct (N × H) |
| 70. D53 | #1712 | direct (N × H) |
| 76. #493 | C2×D53 | semidirect |
| 79. C82 | C2×D53 | semidirect |
| 80. C53 | C2×#1712 | semidirect |
| 119. C8 | D8×D53 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #493×D53 | 2 |
| #20274330 | 2 |
| #20274329 | 2 |
| C82×D53 | 2 |
| C53×#1712 | 2 |
| C2×#1712 | 53 |