Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
1072 conjugacy classes of subgroups; only the 175 normal subgroups are shown.
This group has 1072 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 |
| 3. #20284533 | C2 | semidirect |
| 4. #20275925 | C2 | semidirect |
| 5. #20275696 | C2 | semidirect |
| 6. #20275556 | C2 | semidirect |
| 7. #20274924 | C2 | semidirect |
| 8. #20274526 | C2 | semidirect |
| 9. C53×#2641 | C2 | semidirect |
| 137. #11719917 | #41 | semidirect |
| 198. #2641 | D53 | semidirect |
| 236. C53 | #25690 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20288589 | 2 |
| #20285264 | 2 |
| #20284533 | 2 |
| #20275925 | 2 |
| #20275696 | 2 |
| #20275556 | 2 |
| #20274924 | 2 |
| #20274526 | 2 |
| C53×#2641 | 2 |
| #25690 | 53 |