Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
390 conjugacy classes of subgroups; only the 63 normal subgroups are shown.
This group has 390 conjugacy classes of subgroups — too many to draw. Only its 63 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 |
|---|---|---|
| 1. #20286056 | C2 | semidirect |
| 4. #20272728 | C2 | semidirect |
| 5. #20272727 | C2 | semidirect |
| 6. #20272654 | C2 | semidirect |
| 140. C2×Dic53 | SD32 | semidirect |
| 202. C53 | #12159 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20286056 | 2 |
| #20276644 | 2 |
| #20276023 | 2 |
| #20272728 | 2 |
| #20272727 | 2 |
| #20272654 | 2 |
| C53×#2187 | 2 |
| #12159 | 53 |