Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
620 conjugacy classes of subgroups; only the 113 normal subgroups are shown.
This group has 620 conjugacy classes of subgroups — too many to draw. Only its 113 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. #20277623 | C2 | semidirect |
| 3. #20273210 | C2 | semidirect |
| 4. #20273107 | C2 | semidirect |
| 5. #20272617 | C2 | semidirect |
| 6. #20272573 | C2 | semidirect |
| 7. C53×#1517 | C2 | semidirect |
| 12. #16810825 | C4 | semidirect |
| 13. #16810815 | C4 | semidirect |
| 51. C4⋊#88322 | C2×C4 | semidirect |
| 60. C4⋊Q8×C53 | C2×C4 | semidirect |
| 61. #127×C53 | C2×C4 | semidirect |
| 210. #1517 | D53 | semidirect |
| 243. C53 | #9179 | semidirect |
| 253. C4⋊Q8 | C4×D53 | semidirect |
| 254. #127 | C4×D53 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20284175 | 2 |
| #20277623 | 2 |
| #20273210 | 2 |
| #20273107 | 2 |
| #20272617 | 2 |
| #20272573 | 2 |
| C53×#1517 | 2 |
| #9179 | 53 |