Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
12190 conjugacy classes of subgroups; only the 4939 normal subgroups are shown.
This group has 12190 conjugacy classes of subgroups — too many to draw. Only its 4939 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. C22×#13133215 | C2 | direct (N × H) |
| 10. C2×#13133215 | C22 | direct (N × H) |
| 20. C23×Dic53 | Q8 | semidirect |
| 23. #13133215 | C23 | direct (N × H) |
| 43. C22×Dic53 | C2×Q8 | semidirect |
| 50. C23×C53 | C4⋊Q8 | semidirect |
| 60. C2×Dic53 | C22×Q8 | semidirect |
| 65. C22×C53 | C2×C4⋊Q8 | semidirect |
| 72. Dic53 | C23×Q8 | semidirect |
| 78. C2×C53 | C22×C4⋊Q8 | semidirect |
| 92. C53 | C23×C4⋊Q8 | semidirect |
| 126. C23 | #13133215 | direct (N × H) |
| 140. C22 | C2×#13133215 | direct (N × H) |
| 148. C2 | C22×#13133215 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C24×Dic106 | 2 |
| C22×#13133215 | 2 |
| C23×#11719919 | 2 |
| C23×C4×Dic53 | 2 |
| C24×Q8×C53 | 2 |
| C23×C4⋊Q8 | 53 |