Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
1006 conjugacy classes of subgroups; only the 459 normal subgroups are shown.
This group has 1006 conjugacy classes of subgroups — too many to draw. Only its 459 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 |
|---|---|---|
| 27. C4×C8×C53 | Q8 | semidirect |
| 57. C8×C53 | C4⋊Q8 | semidirect |
| 65. C4×C53 | #500 | semidirect |
| 85. C53 | #33312 | semidirect |
| 98. C4×C8 | Dic106 | semidirect |
| 129. C8 | #13133217 | semidirect |
| 137. C4 | #16811028 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16811028 | 2 |
| #20283113 | 2 |
| #20274875 | 2 |
| C42×C8×C53 | 2 |
| #33312 | 53 |