Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
350 conjugacy classes of subgroups; only the 108 normal subgroups are shown.
This group has 350 conjugacy classes of subgroups — too many to draw. Only its 108 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. #20289733 | C2 | semidirect |
| 122. D53 | #1364 | semidirect |
| 138. C53 | C2×#1364 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D53⋊(C4⋊C16) | 2 |
| D53⋊#335 | 2 |
| #20289733 | 2 |
| #500×D53 | 2 |
| C2×#1364 | 53 |