Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
4126 conjugacy classes of subgroups; only the 2232 normal subgroups are shown.
This group has 4126 conjugacy classes of subgroups — too many to draw. Only its 2232 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×#13133272 | C2 | direct (N × H) |
| 4. C23×#88324 | C4 | semidirect |
| 6. C2×#13133272 | C22 | direct (N × H) |
| 12. C22×#88324 | C2×C4 | semidirect |
| 14. #13133272 | C23 | direct (N × H) |
| 37. C2×#88324 | C22×C4 | semidirect |
| 41. C23×C53 | #97 | semidirect |
| 54. #88324 | C23×C4 | semidirect |
| 56. C22×C53 | C2×#97 | semidirect |
| 68. C2×C53 | C22×#97 | semidirect |
| 80. C53 | C23×#97 | semidirect |
| 110. C23 | #13133272 | direct (N × H) |
| 124. C22 | C2×#13133272 | direct (N × H) |
| 133. C2 | C22×#13133272 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C24×#88324 | 2 |
| C22×#13133272 | 2 |
| C23×C4×Dic53 | 2 |
| C23×#97 | 53 |