Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
388 conjugacy classes of subgroups; only the 95 normal subgroups are shown.
This group has 388 conjugacy classes of subgroups — too many to draw. Only its 95 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 |
|---|---|---|
| 4. #20272657 | C2 | semidirect |
| 5. #20272656 | C2 | semidirect |
| 6. #20272656 | C2 | semidirect |
| 7. C53×#1323 | C2 | semidirect |
| 167. #1323 | D53 | semidirect |
| 193. C53 | #11444 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #424×D53 | 2 |
| #20276324 | 2 |
| C22⋊C16×D53 | 2 |
| #20272657 | 2 |
| #20272656 | 2 |
| C53×#1323 | 2 |
| #11444 | 53 |