Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
528 conjugacy classes of subgroups; only the 113 normal subgroups are shown.
This group has 528 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 |
|---|---|---|
| 2. C2×#16810658 | C2 | semidirect |
| 3. C2×#16810434 | C2 | semidirect |
| 4. C2×#16810432 | C2 | semidirect |
| 5. #20276325 | C2 | semidirect |
| 6. #20272820 | C2 | semidirect |
| 7. C53×#1386 | C2 | semidirect |
| 13. #16810865 | C4 | semidirect |
| 14. #16810860 | C4 | semidirect |
| 58. #13133149 | D4 | semidirect |
| 70. #106×C53 | D4 | semidirect |
| 190. #1386 | D53 | semidirect |
| 216. C53 | #13002 | semidirect |
| 258. #106 | D212 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20284297 | 2 |
| C2×#16810658 | 2 |
| C2×#16810434 | 2 |
| C2×#16810432 | 2 |
| #20276325 | 2 |
| #20272820 | 2 |
| C53×#1386 | 2 |
| #13002 | 53 |