Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
7134 conjugacy classes of subgroups; only the 1208 normal subgroups are shown.
This group has 7134 conjugacy classes of subgroups — too many to draw. Only its 1208 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. C23×#11719940 | C2 | semidirect |
| 2. C22×#13133277 | C2 | direct (N × H) |
| 5. C22×#11719940 | C22 | semidirect |
| 7. C2×#13133277 | C22 | direct (N × H) |
| 16. C2×#11719940 | C23 | semidirect |
| 18. #13133277 | C23 | direct (N × H) |
| 67. #11719940 | C24 | semidirect |
| 76. C23×C53 | #100 | semidirect |
| 103. C22×C53 | C2×#100 | semidirect |
| 119. C2×C53 | C22×#100 | semidirect |
| 133. C53 | C23×#100 | semidirect |
| 201. C23 | #13133277 | direct (N × H) |
| 225. C22 | C2×#13133277 | direct (N × H) |
| 235. C2 | C22×#13133277 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×#11719940 | 2 |
| C22×#13133277 | 2 |
| C24×C22⋊D53 | 2 |
| C23×#100 | 53 |