Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
558 conjugacy classes of subgroups; only the 151 normal subgroups are shown.
This group has 558 conjugacy classes of subgroups — too many to draw. Only its 151 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. #20285299 | C2 | semidirect |
| 3. #20276995 | C2 | semidirect |
| 4. #20276972 | C2 | semidirect |
| 5. #20276939 | C2 | semidirect |
| 6. #20276814 | C2 | semidirect |
| 7. #20276564 | C2 | semidirect |
| 8. C4×C16×D53 | C2 | semidirect |
| 9. C53×#2241 | C2 | semidirect |
| 113. #11719908 | #41 | semidirect |
| 137. C4×D53 | SD32 | semidirect |
| 165. #2241 | D53 | semidirect |
| 200. C53 | #33736 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20285299 | 2 |
| #20285295 | 2 |
| #20276995 | 2 |
| #20276972 | 2 |
| #20276939 | 2 |
| #20276814 | 2 |
| #20276564 | 2 |
| C4×C16×D53 | 2 |
| C53×#2241 | 2 |
| #33736 | 53 |