Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
822 conjugacy classes of subgroups; only the 167 normal subgroups are shown.
This group has 822 conjugacy classes of subgroups — too many to draw. Only its 167 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. C53⋊#2104 | C2 | semidirect |
| 3. C53×#2104 | C2 | semidirect |
| 51. #2104 | D53 | direct (N × H) |
| 56. D53 | #2104 | direct (N × H) |
| 61. C53 | C2×#2104 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C53⋊#2104 | 2 |
| #342×D53 | 2 |
| C53×#2104 | 2 |
| C2×#2104 | 53 |