Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
494 conjugacy classes of subgroups; only the 112 normal subgroups are shown.
This group has 494 conjugacy classes of subgroups — too many to draw. Only its 112 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 |
|---|---|---|
| 1. C2×D53⋊M32 | C2 | semidirect |
| 2. C2×#16811521 | C2 | semidirect |
| 3. C2×#16811518 | C2 | semidirect |
| 4. #20289770 | C2 | semidirect |
| 27. #13133291 | D4 | semidirect |
| 166. C2×D53 | #350 | semidirect |
| 206. C53 | #12978 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×D53⋊M32 | 2 |
| C2×#16811521 | 2 |
| C2×#16811518 | 2 |
| #20289770 | 2 |
| #20283412 | 2 |
| #12978 | 53 |