Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
334 conjugacy classes of subgroups; only the 43 normal subgroups are shown.
This group has 334 conjugacy classes of subgroups — too many to draw. Only its 43 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 |
|---|---|---|
| 1. #20272840 | C2 | semidirect |
| 2. #20272647 | C2 | semidirect |
| 7. C2×#127×C53 | C4 | semidirect |
| 10. C53×#336 | C4 | semidirect |
| 130. C2×#127 | Dic53 | semidirect |
| 134. #336 | Dic53 | semidirect |
| 136. C53 | #7402 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20272840 | 2 |
| #20272647 | 2 |
| C53×#2011 | 2 |
| #7402 | 53 |