Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
1738 conjugacy classes of subgroups; only the 587 normal subgroups are shown.
This group has 1738 conjugacy classes of subgroups — too many to draw. Only its 587 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. #20280680 | C2 | semidirect |
| 2. #20280675 | C2 | semidirect |
| 3. #20280668 | C2 | semidirect |
| 4. #20278013 | C2 | semidirect |
| 6. #20277198 | C2 | semidirect |
| 7. C2×C53×#376 | C2 | semidirect |
| 104. C2×#376 | D53 | semidirect |
| 126. C53 | #34639 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20280680 | 2 |
| #20280675 | 2 |
| #20280668 | 2 |
| #20278013 | 2 |
| #20277205 | 2 |
| #20277198 | 2 |
| C2×C53×#376 | 2 |
| #34639 | 53 |