Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
12190 conjugacy classes of subgroups; only the 5451 normal subgroups are shown.
This group has 12190 conjugacy classes of subgroups — too many to draw. Only its 5451 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×#13133217 | C2 | direct (N × H) |
| 8. C2×#13133217 | C22 | direct (N × H) |
| 17. #13133217 | C23 | direct (N × H) |
| 21. C23×C4×C53 | Q8 | semidirect |
| 29. C22×C4×C53 | C2×Q8 | semidirect |
| 38. C23×C53 | C4⋊Q8 | semidirect |
| 43. C2×C4×C53 | C22×Q8 | semidirect |
| 50. C22×C53 | C2×C4⋊Q8 | semidirect |
| 55. C4×C53 | C23×Q8 | semidirect |
| 61. C2×C53 | C22×C4⋊Q8 | semidirect |
| 72. C53 | C23×C4⋊Q8 | semidirect |
| 78. C23×C4 | Dic106 | semidirect |
| 92. C22×C4 | C2×Dic106 | semidirect |
| 98. C23 | #13133217 | direct (N × H) |
| 106. C2×C4 | C22×Dic106 | semidirect |
| 109. C22 | C2×#13133217 | direct (N × H) |
| 115. C4 | C23×Dic106 | semidirect |
| 116. C2 | C22×#13133217 | 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×#13133217 | 2 |
| C23×C4⋊Dic53 | 2 |
| C23×C42×C53 | 2 |
| C23×C4⋊Q8 | 53 |