Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
510 conjugacy classes of subgroups; only the 147 normal subgroups are shown.
This group has 510 conjugacy classes of subgroups — too many to draw. Only its 147 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 |
|---|---|---|
| 3. C2×#16810400 | C2 | semidirect |
| 4. #20272795 | C2 | semidirect |
| 5. C53×#1375 | C2 | semidirect |
| 14. #16810402 | C4 | semidirect |
| 35. C2×#11719908 | C2×C4 | semidirect |
| 44. C2×C16×C53 | C2×C4 | semidirect |
| 119. C2×D53 | #347 | semidirect |
| 131. #1375 | D53 | semidirect |
| 149. C53 | #12605 | semidirect |
| 173. C2×C16 | C4×D53 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#97×D53 | 2 |
| #20276325 | 2 |
| C2×#16810400 | 2 |
| #20272795 | 2 |
| C53×#1375 | 2 |
| #12605 | 53 |