Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
8414 conjugacy classes of subgroups; only the 4427 normal subgroups are shown.
This group has 8414 conjugacy classes of subgroups — too many to draw. Only its 4427 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. C22×#13133209 | C2 | direct (N × H) |
| 6. C2×#13133209 | C22 | direct (N × H) |
| 14. #13133209 | C23 | direct (N × H) |
| 35. C23×C53 | #125 | semidirect |
| 46. C22×C53 | C2×#125 | semidirect |
| 57. C2×C53 | C22×#125 | semidirect |
| 67. C53 | C23×#125 | semidirect |
| 91. C23 | #13133209 | direct (N × H) |
| 101. C22 | C2×#13133209 | direct (N × H) |
| 108. C2 | C22×#13133209 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#13133209 | 2 |
| C23×C4⋊Dic53 | 2 |
| C23×#11719919 | 2 |
| C23×C42×C53 | 2 |
| C23×#125 | 53 |