Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
400 conjugacy classes of subgroups; only the 69 normal subgroups are shown.
This group has 400 conjugacy classes of subgroups — too many to draw. Only its 69 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. #20286475 | C2 | semidirect |
| 2. #20276965 | C2 | semidirect |
| 3. #20276756 | C2 | semidirect |
| 4. #20274070 | C2 | semidirect |
| 5. #20272762 | C2 | semidirect |
| 6. #20272680 | C2 | semidirect |
| 7. C53×D4⋊C16 | C2 | semidirect |
| 85. Dic212 | D8 | semidirect |
| 153. D4⋊C16 | D53 | semidirect |
| 177. C53 | #12317 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20286475 | 2 |
| #20276965 | 2 |
| #20276756 | 2 |
| #20274070 | 2 |
| #20272762 | 2 |
| #20272680 | 2 |
| C53×D4⋊C16 | 2 |
| #12317 | 53 |