Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
410 conjugacy classes of subgroups; only the 91 normal subgroups are shown.
This group has 410 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 |
|---|---|---|
| 3. #20272666 | C2 | semidirect |
| 4. #20272665 | C2 | semidirect |
| 5. C53×#1327 | C2 | semidirect |
| 157. #1327 | D53 | direct (N × H) |
| 163. D53 | #1327 | direct (N × H) |
| 177. C53 | C2×#1327 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #423×D53 | 2 |
| #349×D53 | 2 |
| #20272666 | 2 |
| #20272665 | 2 |
| C53×#1327 | 2 |
| C2×#1327 | 53 |