Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
694 conjugacy classes of subgroups; only the 171 normal subgroups are shown.
This group has 694 conjugacy classes of subgroups — too many to draw. Only its 171 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. #20276288 | C2 | semidirect |
| 4. #20275684 | C2 | semidirect |
| 5. #20275683 | C2 | semidirect |
| 6. #20274848 | C2 | semidirect |
| 9. C53×#1836 | C2 | semidirect |
| 160. #1836 | D53 | semidirect |
| 190. C53 | #27967 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20283026 | 2 |
| #20277120 | 2 |
| #20276288 | 2 |
| #20275684 | 2 |
| #20275683 | 2 |
| #20274848 | 2 |
| #20274808 | 2 |
| #20274478 | 2 |
| C53×#1836 | 2 |
| #27967 | 53 |