Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
512 conjugacy classes of subgroups; only the 81 normal subgroups are shown.
This group has 512 conjugacy classes of subgroups — too many to draw. Only its 81 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. #20284841 | C2 | semidirect |
| 4. #20273266 | C2 | semidirect |
| 5. #20273163 | C2 | semidirect |
| 6. #20272580 | C2 | semidirect |
| 228. C53 | #10024 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20284841 | 2 |
| #20280576 | 2 |
| #20273339 | 2 |
| #20273266 | 2 |
| #20273163 | 2 |
| #20272580 | 2 |
| C53×#3140 | 2 |
| #10024 | 53 |