Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
1334 conjugacy classes of subgroups; only the 400 normal subgroups are shown.
This group has 1334 conjugacy classes of subgroups — too many to draw. Only its 400 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. C2×#16811483 | C2 | direct (N × H) |
| 7. #16811483 | C22 | direct (N × H) |
| 88. C22×C53 | #333 | semidirect |
| 102. C2×C53 | C2×#333 | semidirect |
| 116. C53 | C22×#333 | semidirect |
| 189. C22 | #16811483 | direct (N × H) |
| 200. C2 | C2×#16811483 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#13133284 | 2 |
| C2×#16811483 | 2 |
| C22×#13133215 | 2 |
| C22×#333 | 53 |