Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
476 conjugacy classes of subgroups; only the 84 normal subgroups are shown.
This group has 476 conjugacy classes of subgroups — too many to draw. Only its 84 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. D53⋊#362 | C2 | semidirect |
| 4. #20290861 | C2 | semidirect |
| 5. #20289790 | C2 | semidirect |
| 6. #20289758 | C2 | semidirect |
| 24. #16811066 | C4 | semidirect |
| 26. #16811064 | C4 | semidirect |
| 27. #16811063 | C4 | semidirect |
| 32. C53×#510 | C4 | semidirect |
| 235. #510 | #6157 | semidirect |
| 252. C53 | #13028 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D53⋊#443 | 2 |
| D53⋊#362 | 2 |
| #20291023 | 2 |
| #20290861 | 2 |
| #20289790 | 2 |
| #20289758 | 2 |
| #510×D53 | 2 |
| #13028 | 53 |