Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
492 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 492 conjugacy classes of subgroups — too many to draw. Only its 107 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 |
|---|---|---|
| 3. #20275656 | C2 | semidirect |
| 5. #20272610 | C2 | semidirect |
| 6. #20272559 | C2 | semidirect |
| 7. C53×#1487 | C2 | semidirect |
| 117. C2×#88322 | SD16 | semidirect |
| 184. #1487 | D53 | semidirect |
| 214. C53 | #9047 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20284746 | 2 |
| #20283432 | 2 |
| #20275656 | 2 |
| #20273362 | 2 |
| #20272610 | 2 |
| #20272559 | 2 |
| C53×#1487 | 2 |
| #9047 | 53 |