Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
402 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 402 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 |
|---|---|---|
| 107. #11719917 | Q16 | semidirect |
| 198. C53 | #10505 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20275705 | 2 |
| #20275660 | 2 |
| #20275639 | 2 |
| #20273468 | 2 |
| #20273405 | 2 |
| #20272617 | 2 |
| C53×#3209 | 2 |
| #10505 | 53 |