Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
1124 conjugacy classes of subgroups; only the 195 normal subgroups are shown.
This group has 1124 conjugacy classes of subgroups — too many to draw. Only its 195 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. C23×Dic212 | C2 | semidirect |
| 2. C2×#16811066 | C2 | semidirect |
| 4. #20276651 | C2 | semidirect |
| 5. #20276634 | C2 | semidirect |
| 6. #20276436 | C2 | semidirect |
| 7. C53×#2112 | C2 | semidirect |
| 17. C2×Dic424 | C22 | semidirect |
| 18. C2×#13133162 | C22 | semidirect |
| 24. #16810428 | C22 | semidirect |
| 43. C2×Dic212 | D4 | semidirect |
| 154. C22×C53 | #510 | semidirect |
| 171. #2112 | D53 | semidirect |
| 197. C53 | #33518 | semidirect |
| 325. C22 | #16811066 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×Dic212 | 2 |
| C2×#16811066 | 2 |
| #20284296 | 2 |
| #20276651 | 2 |
| #20276634 | 2 |
| #20276436 | 2 |
| C53×#2112 | 2 |
| #33518 | 53 |