Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
636 conjugacy classes of subgroups; only the 135 normal subgroups are shown.
This group has 636 conjugacy classes of subgroups — too many to draw. Only its 135 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. #20287864 | C2 | semidirect |
| 2. #20286519 | C2 | semidirect |
| 3. #20276837 | C2 | semidirect |
| 4. #20276793 | C2 | semidirect |
| 5. #20276692 | C2 | semidirect |
| 6. #20276597 | C2 | semidirect |
| 7. #20276553 | C2 | semidirect |
| 8. C53×#2247 | C2 | semidirect |
| 137. #2247 | D53 | semidirect |
| 169. C53 | #33860 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20287864 | 2 |
| #20286519 | 2 |
| #20276837 | 2 |
| #20276793 | 2 |
| #20276692 | 2 |
| #20276597 | 2 |
| #20276553 | 2 |
| C53×#2247 | 2 |
| #33860 | 53 |