Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
474 conjugacy classes of subgroups; only the 90 normal subgroups are shown.
This group has 474 conjugacy classes of subgroups — too many to draw. Only its 90 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 |
|---|---|---|
| 25. #16810915 | C4 | semidirect |
| 26. #16810834 | C4 | semidirect |
| 27. #16810833 | C4 | semidirect |
| 32. C53×#477 | C4 | semidirect |
| 109. C4×#6157 | Q16 | semidirect |
| 222. #477 | #6157 | semidirect |
| 243. C53 | #9236 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20291174 | 2 |
| #20290900 | 2 |
| #20290099 | 2 |
| #20290044 | 2 |
| #20289612 | 2 |
| #20289542 | 2 |
| #20284756 | 2 |
| #9236 | 53 |