Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
920 conjugacy classes of subgroups; only the 175 normal subgroups are shown.
This group has 920 conjugacy classes of subgroups — too many to draw. Only its 175 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 |
|---|---|---|
| 2. #20285264 | C2 | semidirect |
| 5. #20275696 | C2 | semidirect |
| 6. #20275560 | C2 | semidirect |
| 7. #20274929 | C2 | semidirect |
| 9. C53×#2642 | C2 | semidirect |
| 188. #2642 | D53 | semidirect |
| 225. C53 | #25691 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20288599 | 2 |
| #20285264 | 2 |
| #20284533 | 2 |
| #20275932 | 2 |
| #20275696 | 2 |
| #20275560 | 2 |
| #20274929 | 2 |
| #20274526 | 2 |
| C53×#2642 | 2 |
| #25691 | 53 |