Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
4126 conjugacy classes of subgroups; only the 2795 normal subgroups are shown.
This group has 4126 conjugacy classes of subgroups — too many to draw. Only its 2795 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×#13133128 | C2 | direct (N × H) |
| 4. C23×#88322 | C4 | semidirect |
| 6. C2×#13133128 | C22 | direct (N × H) |
| 11. C22×#88322 | C2×C4 | semidirect |
| 13. #13133128 | C23 | direct (N × H) |
| 33. C2×#88322 | C22×C4 | semidirect |
| 35. C23×C53 | #97 | semidirect |
| 45. #88322 | C23×C4 | semidirect |
| 47. C22×C53 | C2×#97 | semidirect |
| 57. C2×C53 | C22×#97 | semidirect |
| 67. C53 | C23×#97 | semidirect |
| 92. C23 | #13133128 | direct (N × H) |
| 103. C22 | C2×#13133128 | direct (N × H) |
| 110. C2 | C22×#13133128 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C24×#88322 | 2 |
| C22×#13133128 | 2 |
| C23×C42×C53 | 2 |
| C23×#97 | 53 |