Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
1158 conjugacy classes of subgroups; only the 272 normal subgroups are shown.
This group has 1158 conjugacy classes of subgroups — too many to draw. Only its 272 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 |
|---|---|---|
| 2. D53⋊#330 | C2 | direct (N × H) |
| 3. C2×#16811480 | C2 | semidirect |
| 10. #16811480 | C22 | semidirect |
| 121. C2×D53 | #330 | semidirect |
| 136. C2×C53 | C2×#330 | semidirect |
| 139. D53 | C2×#330 | semidirect |
| 156. C53 | C22×#330 | semidirect |
| 268. C2 | D53⋊#330 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16811582 | 2 |
| D53⋊#330 | 2 |
| C2×#16811480 | 2 |
| C2×#125×D53 | 2 |
| C22×#330 | 53 |