Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
446 conjugacy classes of subgroups; only the 88 normal subgroups are shown.
This group has 446 conjugacy classes of subgroups — too many to draw. Only its 88 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. #20289708 | C2 | semidirect |
| 4. #20289707 | C2 | semidirect |
| 171. D53 | #1350 | semidirect |
| 189. C53 | C2×#1350 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D53⋊(C22⋊C16) | 2 |
| #20290407 | 2 |
| #20289708 | 2 |
| #20289707 | 2 |
| #467×D53 | 2 |
| C2×#1350 | 53 |