Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
420 conjugacy classes of subgroups; only the 115 normal subgroups are shown.
This group has 420 conjugacy classes of subgroups — too many to draw. Only its 115 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. #20274761 | C2 | semidirect |
| 3. #20272836 | C2 | semidirect |
| 10. C2×#131×C53 | C4 | semidirect |
| 15. C53×#423 | C4 | semidirect |
| 16. C53×#408 | C4 | semidirect |
| 18. C2×#97×C53 | C4 | semidirect |
| 140. C2×#131 | Dic53 | semidirect |
| 146. #423 | Dic53 | semidirect |
| 148. #408 | Dic53 | semidirect |
| 150. C2×#97 | Dic53 | semidirect |
| 154. C53 | #12808 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20276380 | 2 |
| #20274761 | 2 |
| #20272836 | 2 |
| C53×#2932 | 2 |
| #12808 | 53 |