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 |
|---|---|---|
| 3. C2×#16811482 | C2 | direct (N × H) |
| 11. #16811482 | C22 | direct (N × H) |
| 117. C22×C53 | #332 | semidirect |
| 136. C2×C53 | C2×#332 | semidirect |
| 156. C53 | C22×#332 | semidirect |
| 252. C22 | #16811482 | direct (N × H) |
| 267. C2 | C2×#16811482 | 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×#16811482 | 2 |
| C22×#13133216 | 2 |
| C22×#332 | 53 |