Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
714 conjugacy classes of subgroups; only the 171 normal subgroups are shown.
This group has 714 conjugacy classes of subgroups — too many to draw. Only its 171 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. C22×D848 | C2 | semidirect |
| 2. C2×#16811039 | C2 | semidirect |
| 3. #20284364 | C2 | semidirect |
| 4. #20276819 | C2 | semidirect |
| 5. #20276802 | C2 | semidirect |
| 6. #20276430 | C2 | semidirect |
| 7. C53×#2158 | C2 | semidirect |
| 16. C2×#13133156 | C22 | semidirect |
| 17. C2×C16×D53 | C22 | semidirect |
| 19. #16810860 | C22 | semidirect |
| 21. #16810423 | C22 | semidirect |
| 24. C53×#367 | C22 | semidirect |
| 25. C53×#366 | C22 | semidirect |
| 50. C2×C16×C53 | D4 | semidirect |
| 130. #2158 | D53 | semidirect |
| 152. #367 | C2×D53 | semidirect |
| 153. #366 | C2×D53 | semidirect |
| 155. C53 | #33607 | semidirect |
| 179. C2×C16 | D212 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×D848 | 2 |
| C2×#16811039 | 2 |
| #20284364 | 2 |
| #20276819 | 2 |
| #20276802 | 2 |
| #20276430 | 2 |
| C53×#2158 | 2 |
| #33607 | 53 |