Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
380 conjugacy classes of subgroups; only the 127 normal subgroups are shown.
This group has 380 conjugacy classes of subgroups — too many to draw. Only its 127 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. #20272822 | C2 | semidirect |
| 4. #20272816 | C2 | semidirect |
| 15. C53×#427 | C4 | semidirect |
| 17. C2×#106×C53 | C4 | semidirect |
| 129. #427 | Dic53 | semidirect |
| 131. C2×#106 | Dic53 | semidirect |
| 136. C53 | #12873 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20276336 | 2 |
| #20274761 | 2 |
| #20272822 | 2 |
| #20272816 | 2 |
| C53×#2912 | 2 |
| #12873 | 53 |