Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
346 conjugacy classes of subgroups; only the 111 normal subgroups are shown.
This group has 346 conjugacy classes of subgroups — too many to draw. Only its 111 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 |
|---|---|---|
| 12. C53×#500 | C4 | semidirect |
| 13. C53×#494 | C4 | semidirect |
| 18. C4×Q16×C53 | C4 | semidirect |
| 123. #500 | Dic53 | semidirect |
| 124. #494 | Dic53 | semidirect |
| 129. C4×Q16 | Dic53 | semidirect |
| 137. C53 | #11745 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20276518 | 2 |
| C4×#13133149 | 2 |
| #20272727 | 2 |
| C53×#3170 | 2 |
| #11745 | 53 |