Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
478 conjugacy classes of subgroups; only the 103 normal subgroups are shown.
This group has 478 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 |
|---|---|---|
| 2. C4×#13133136 | C2 | semidirect |
| 4. #20272581 | C2 | semidirect |
| 5. C53×#2983 | C2 | semidirect |
| 167. #2983 | D53 | semidirect |
| 197. C53 | #9188 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20280575 | 2 |
| C4×#13133136 | 2 |
| #20273314 | 2 |
| #20272581 | 2 |
| C53×#2983 | 2 |
| #9188 | 53 |