Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
3614 conjugacy classes of subgroups; only the 1464 normal subgroups are shown.
This group has 3614 conjugacy classes of subgroups — too many to draw. Only its 1464 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×#13133285 | C2 | direct (N × H) |
| 7. C2×#13133285 | C22 | direct (N × H) |
| 9. C23×#88322 | C4 | semidirect |
| 10. C22×C8×D53 | C4 | semidirect |
| 12. C23×C8×C53 | C4 | semidirect |
| 17. #13133285 | C23 | direct (N × H) |
| 24. C22×#88322 | C2×C4 | semidirect |
| 25. C2×C8×D53 | C2×C4 | semidirect |
| 28. C22×C8×C53 | C2×C4 | semidirect |
| 46. C2×C8×C53 | C22×C4 | semidirect |
| 47. C2×#88322 | C22×C4 | semidirect |
| 48. C8×D53 | C22×C4 | semidirect |
| 50. C23×C53 | #106 | semidirect |
| 52. C22×D53 | #106 | semidirect |
| 67. C8×C53 | C23×C4 | semidirect |
| 68. #88322 | C23×C4 | semidirect |
| 70. C22×C53 | C2×#106 | semidirect |
| 72. C2×D53 | C2×#106 | semidirect |
| 84. C2×C53 | C22×#106 | semidirect |
| 86. D53 | C22×#106 | semidirect |
| 93. C23×C8 | #6157 | semidirect |
| 97. C53 | C23×#106 | semidirect |
| 110. C22×C8 | C2×#6157 | semidirect |
| 132. C2×C8 | C22×#6157 | semidirect |
| 139. C23 | #13133285 | direct (N × H) |
| 153. C8 | C23×#6157 | semidirect |
| 158. C22 | C2×#13133285 | direct (N × H) |
| 167. C2 | C22×#13133285 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×C4⋊#6157 | 2 |
| C22×#13133285 | 2 |
| C23×C8×D53 | 2 |
| C23×#106 | 53 |