Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
512 conjugacy classes of subgroups; only the 84 normal subgroups are shown.
This group has 512 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 |
|---|---|---|
| 1. D53⋊#443 | C2 | semidirect |
| 2. D53⋊#361 | C2 | semidirect |
| 3. #20291023 | C2 | semidirect |
| 4. #20290862 | C2 | semidirect |
| 5. #20289790 | C2 | semidirect |
| 6. #20289758 | C2 | semidirect |
| 24. #16811061 | C4 | semidirect |
| 26. #16811059 | C4 | semidirect |
| 27. #16811058 | C4 | semidirect |
| 32. C53×#509 | C4 | semidirect |
| 124. Q16×C53 | C22⋊C4 | semidirect |
| 128. D8×C53 | C22⋊C4 | semidirect |
| 137. Dic212 | C22⋊C4 | semidirect |
| 140. D424 | C22⋊C4 | semidirect |
| 245. #509 | #6157 | semidirect |
| 262. C53 | #13029 | semidirect |
| 340. Q16 | C22⋊#6157 | semidirect |
| 353. D8 | C22⋊#6157 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D53⋊#443 | 2 |
| D53⋊#361 | 2 |
| #20291023 | 2 |
| #20290862 | 2 |
| #20289790 | 2 |
| #20289758 | 2 |
| #509×D53 | 2 |
| #13029 | 53 |