Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
632 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 632 conjugacy classes of subgroups — too many to draw. Only its 107 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. #20277438 | C2 | semidirect |
| 3. #20275548 | C2 | semidirect |
| 4. #20273382 | C2 | semidirect |
| 5. #20272573 | C2 | semidirect |
| 6. #20272543 | C2 | semidirect |
| 7. C53×#1517 | C2 | semidirect |
| 10. #16810999 | C4 | semidirect |
| 11. #16810971 | C4 | semidirect |
| 51. C4×#88322 | C2×C4 | semidirect |
| 55. C4⋊Q8×C53 | C2×C4 | semidirect |
| 56. #127×C53 | C2×C4 | semidirect |
| 119. C4×Dic53 | D8 | semidirect |
| 209. #1517 | D53 | semidirect |
| 238. C53 | #9299 | semidirect |
| 246. C4⋊Q8 | C4×D53 | semidirect |
| 251. #127 | C4×D53 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20285630 | 2 |
| #20277438 | 2 |
| #20275548 | 2 |
| #20273382 | 2 |
| #20272573 | 2 |
| #20272543 | 2 |
| C53×#1517 | 2 |
| #9299 | 53 |