Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
972 conjugacy classes of subgroups; only the 205 normal subgroups are shown.
This group has 972 conjugacy classes of subgroups — too many to draw. Only its 205 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. #430×D53 | C2 | semidirect |
| 3. #20276232 | C2 | semidirect |
| 4. #20276231 | C2 | semidirect |
| 5. #20276230 | C2 | semidirect |
| 6. #338×D53 | C2 | semidirect |
| 7. C53×#2091 | C2 | semidirect |
| 153. #2091 | D53 | semidirect |
| 177. C53 | #23723 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #430×D53 | 2 |
| #20283158 | 2 |
| #20276232 | 2 |
| #20276231 | 2 |
| #20276230 | 2 |
| #338×D53 | 2 |
| C53×#2091 | 2 |
| #23723 | 53 |