Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
630 conjugacy classes of subgroups; only the 139 normal subgroups are shown.
This group has 630 conjugacy classes of subgroups — too many to draw. Only its 139 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. #20273107 | C2 | semidirect |
| 3. #20273036 | C2 | semidirect |
| 4. #20272543 | C2 | semidirect |
| 5. C53×#2972 | C2 | semidirect |
| 25. #13133213 | C8 | semidirect |
| 51. C4×C8×C53 | D4 | semidirect |
| 74. C2×D212 | C2×C8 | semidirect |
| 90. C4×Dic53 | C2×C8 | semidirect |
| 157. #2972 | D53 | semidirect |
| 184. C53 | #9101 | semidirect |
| 212. C4×C8 | C22⋊D53 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20277437 | 2 |
| #20273107 | 2 |
| #20273036 | 2 |
| #20272543 | 2 |
| C53×#2972 | 2 |
| #9101 | 53 |