Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
594 conjugacy classes of subgroups; only the 109 normal subgroups are shown.
This group has 594 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 |
|---|---|---|
| 4. #20273279 | C2 | semidirect |
| 5. #20272575 | C2 | semidirect |
| 6. #20272544 | C2 | semidirect |
| 7. C53×#1995 | C2 | semidirect |
| 10. #16810997 | C4 | semidirect |
| 11. #16810971 | C4 | semidirect |
| 48. C4×#88322 | C2×C4 | semidirect |
| 52. C4⋊Q8×C53 | C2×C4 | semidirect |
| 53. C4⋊Q8×C53 | C2×C4 | semidirect |
| 105. C42×C53 | SD16 | semidirect |
| 191. #1995 | D53 | semidirect |
| 221. C53 | #9295 | semidirect |
| 228. C4⋊Q8 | C4×D53 | semidirect |
| 229. C4⋊Q8 | C4×D53 | semidirect |
| 308. C42 | #11719924 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20285653 | 2 |
| #20277440 | 2 |
| #20273384 | 2 |
| #20273279 | 2 |
| #20272575 | 2 |
| #20272544 | 2 |
| C53×#1995 | 2 |
| #9295 | 53 |