Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
306 conjugacy classes of subgroups; only the 92 normal subgroups are shown.
This group has 306 conjugacy classes of subgroups — too many to draw. Only its 92 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 |
|---|---|---|
| 3. #20289734 | C2 | semidirect |
| 4. #20289733 | C2 | semidirect |
| 152. C53 | #11939 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D53⋊(C4⋊C16) | 2 |
| #20290263 | 2 |
| #20289734 | 2 |
| #20289733 | 2 |
| #20285228 | 2 |
| #11939 | 53 |