Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
620 conjugacy classes of subgroups; only the 103 normal subgroups are shown.
This group has 620 conjugacy classes of subgroups — too many to draw. Only its 103 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. #20277892 | C2 | semidirect |
| 2. #20273429 | C2 | semidirect |
| 3. #20273262 | C2 | semidirect |
| 4. #20272580 | C2 | semidirect |
| 16. C53×#493 | C4 | semidirect |
| 17. C53×#492 | C4 | semidirect |
| 36. C4⋊Q8×C53 | C2×C4 | semidirect |
| 39. #127×C53 | C2×C4 | semidirect |
| 46. C4×C8×C53 | C2×C4 | semidirect |
| 140. #493 | Dic53 | semidirect |
| 141. #492 | Dic53 | semidirect |
| 149. C53 | #9428 | semidirect |
| 159. C4⋊Q8 | C2×Dic53 | semidirect |
| 162. #127 | C2×Dic53 | semidirect |
| 174. C4×C8 | C2×Dic53 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20277892 | 2 |
| #20273429 | 2 |
| #20273262 | 2 |
| #20272580 | 2 |
| C53×#3151 | 2 |
| #9428 | 53 |