Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
284 conjugacy classes of subgroups; only the 91 normal subgroups are shown.
This group has 284 conjugacy classes of subgroups — too many to draw. Only its 91 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 |
|---|---|---|
| 18. #13133136 | C8 | semidirect |
| 127. C53 | #7206 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×#13133136 | 2 |
| #20273039 | 2 |
| C53×#1984 | 2 |
| #7206 | 53 |