Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
1134 conjugacy classes of subgroups; only the 371 normal subgroups are shown.
This group has 1134 conjugacy classes of subgroups — too many to draw. Only its 371 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 |
|---|---|---|
| 2. #20274858 | C2 | semidirect |
| 3. #20274857 | C2 | semidirect |
| 5. C53×#1839 | C2 | semidirect |
| 31. C42×D53 | C8 | semidirect |
| 53. C42×C53 | C2×C8 | semidirect |
| 60. C4×Dic53 | C2×C8 | semidirect |
| 102. #1839 | D53 | direct (N × H) |
| 107. D53 | #1839 | direct (N × H) |
| 119. C53 | C2×#1839 | semidirect |
| 165. C42 | C8×D53 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C43×D53 | 2 |
| #20274858 | 2 |
| #20274857 | 2 |
| #336×D53 | 2 |
| C53×#1839 | 2 |
| C2×#1839 | 53 |