Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
194 conjugacy classes of subgroups; only the 63 normal subgroups are shown.
This group has 194 conjugacy classes of subgroups — too many to draw. Only its 63 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. #20276592 | C2 | semidirect |
| 3. #20272922 | C2 | semidirect |
| 4. #20272904 | C2 | semidirect |
| 5. #20272902 | C2 | semidirect |
| 6. #20272851 | C2 | semidirect |
| 7. C53×#2179 | C2 | semidirect |
| 10. #16810460 | C4 | semidirect |
| 11. #16810458 | C4 | semidirect |
| 28. #13133123 | C2×C4 | semidirect |
| 31. Q32×C53 | C2×C4 | semidirect |
| 33. D16×C53 | C2×C4 | semidirect |
| 85. #2179 | D53 | semidirect |
| 108. C53 | #13658 | semidirect |
| 113. Q32 | C4×D53 | semidirect |
| 117. D16 | C4×D53 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20277027 | 2 |
| #20276592 | 2 |
| #20272922 | 2 |
| #20272904 | 2 |
| #20272902 | 2 |
| #20272851 | 2 |
| C53×#2179 | 2 |
| #13658 | 53 |