Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
476 conjugacy classes of subgroups; only the 105 normal subgroups are shown.
This group has 476 conjugacy classes of subgroups — too many to draw. Only its 105 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. #20283600 | C2 | semidirect |
| 3. #20276450 | C2 | semidirect |
| 4. C2×#16810433 | C2 | semidirect |
| 5. #20272820 | C2 | semidirect |
| 6. #20272801 | C2 | semidirect |
| 7. C53×#1976 | C2 | semidirect |
| 10. #16811064 | C4 | semidirect |
| 12. #16811059 | C4 | semidirect |
| 50. #13133157 | C2×C4 | semidirect |
| 62. C2×Q16×C53 | C2×C4 | semidirect |
| 64. C2×D8×C53 | C2×C4 | semidirect |
| 188. #1976 | D53 | semidirect |
| 218. C53 | #13030 | semidirect |
| 230. C2×Q16 | C4×D53 | semidirect |
| 234. C2×D8 | C4×D53 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20287849 | 2 |
| #20283600 | 2 |
| #20276450 | 2 |
| C2×#16810433 | 2 |
| #20272820 | 2 |
| #20272801 | 2 |
| C53×#1976 | 2 |
| #13030 | 53 |