Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
568 conjugacy classes of subgroups; only the 95 normal subgroups are shown.
This group has 568 conjugacy classes of subgroups — too many to draw. Only its 95 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. #20287849 | C2 | semidirect |
| 2. C2×#16811061 | C2 | semidirect |
| 3. #20285202 | C2 | semidirect |
| 4. #20276430 | C2 | semidirect |
| 5. #20275611 | C2 | semidirect |
| 6. #20272802 | C2 | semidirect |
| 7. C53×#2145 | C2 | semidirect |
| 41. C2×Dic212 | D4 | semidirect |
| 50. C2×D424 | D4 | semidirect |
| 66. C2×#11719908 | D4 | semidirect |
| 82. M32×C53 | D4 | semidirect |
| 214. #2145 | D53 | semidirect |
| 250. C53 | #13334 | semidirect |
| 295. M32 | C22⋊D53 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20287849 | 2 |
| C2×#16811061 | 2 |
| #20285202 | 2 |
| #20276430 | 2 |
| #20275611 | 2 |
| #20272802 | 2 |
| C53×#2145 | 2 |
| #13334 | 53 |