Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
1134 conjugacy classes of subgroups; only the 360 normal subgroups are shown.
This group has 1134 conjugacy classes of subgroups — too many to draw. Only its 360 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. #20290643 | C2 | semidirect |
| 2. #20290642 | C2 | semidirect |
| 29. C42×D53 | C8 | semidirect |
| 51. C42×C53 | C2×C8 | semidirect |
| 58. C4×Dic53 | C2×C8 | semidirect |
| 101. D53 | #1839 | semidirect |
| 112. C53 | C2×#1839 | semidirect |
| 156. C42 | D53⋊C8 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20290643 | 2 |
| #20290642 | 2 |
| #20290376 | 2 |
| C43×D53 | 2 |
| C2×#1839 | 53 |