Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
492 conjugacy classes of subgroups; only the 113 normal subgroups are shown.
This group has 492 conjugacy classes of subgroups — too many to draw. Only its 113 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. #20276434 | C2 | semidirect |
| 4. C2×#16810428 | C2 | semidirect |
| 6. #20272825 | C2 | semidirect |
| 7. C53×#1382 | C2 | semidirect |
| 14. #16810899 | C4 | semidirect |
| 38. C2×Dic212 | C2×C4 | semidirect |
| 68. #108×C53 | C2×C4 | semidirect |
| 182. #1382 | D53 | semidirect |
| 209. C53 | #12997 | semidirect |
| 245. #108 | C4×D53 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16810899 | 2 |
| #20283312 | 2 |
| #20276434 | 2 |
| C2×#16810428 | 2 |
| C2×#16810406 | 2 |
| #20272825 | 2 |
| C53×#1382 | 2 |
| #12997 | 53 |