Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
542 conjugacy classes of subgroups; only the 177 normal subgroups are shown.
This group has 542 conjugacy classes of subgroups — too many to draw. Only its 177 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. #20272996 | C2 | semidirect |
| 4. #20272564 | C2 | semidirect |
| 28. #13133134 | C8 | semidirect |
| 62. #11719917 | C2×C8 | semidirect |
| 99. #88322 | #100 | semidirect |
| 142. C53 | C8×#100 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×D4×#88322 | 2 |
| C4×#13133134 | 2 |
| #20272996 | 2 |
| #20272564 | 2 |
| C53×#1460 | 2 |
| C8×#100 | 53 |