Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
254 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 254 conjugacy classes of subgroups — too many to draw. Only its 99 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 |
|---|---|---|
| 13. #16810447 | C4 | semidirect |
| 128. C53 | #13117 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20276489 | 2 |
| #20275463 | 2 |
| #20272829 | 2 |
| #20272826 | 2 |
| #20272818 | 2 |
| #20272797 | 2 |
| C4×#108×C53 | 2 |
| #13117 | 53 |