Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
466 conjugacy classes of subgroups; only the 82 normal subgroups are shown.
This group has 466 conjugacy classes of subgroups — too many to draw. Only its 82 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. D53⋊#444 | C2 | semidirect |
| 2. #20291043 | C2 | semidirect |
| 3. #20291031 | C2 | semidirect |
| 4. #20290869 | C2 | semidirect |
| 5. #20289793 | C2 | semidirect |
| 6. #20289761 | C2 | semidirect |
| 25. #16811064 | C4 | semidirect |
| 26. #16811061 | C4 | semidirect |
| 28. #16811058 | C4 | semidirect |
| 32. C53×#510 | C4 | semidirect |
| 225. #510 | #6157 | semidirect |
| 245. C53 | #13024 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D53⋊#444 | 2 |
| #20291043 | 2 |
| #20291031 | 2 |
| #20290869 | 2 |
| #20289793 | 2 |
| #20289761 | 2 |
| #20287850 | 2 |
| #13024 | 53 |