Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
294 conjugacy classes of subgroups; only the 80 normal subgroups are shown.
This group has 294 conjugacy classes of subgroups — too many to draw. Only its 80 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⋊C32 | C2 | semidirect |
| 2. C2×#16811551 | C2 | semidirect |
| 3. #20289867 | C2 | direct (N × H) |
| 7. D53⋊C32 | C22 | semidirect |
| 10. #16811551 | C22 | semidirect |
| 111. C2×C53 | #1417 | semidirect |
| 131. C53 | C2×#1417 | semidirect |
| 221. C2 | #20289867 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×D53⋊C32 | 2 |
| C2×#16811551 | 2 |
| #20289867 | 2 |
| C2×#16811056 | 2 |
| C2×#1417 | 53 |