Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
1072 conjugacy classes of subgroups; only the 179 normal subgroups are shown.
This group has 1072 conjugacy classes of subgroups — too many to draw. Only its 179 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. #20285267 | C2 | semidirect |
| 3. #20284538 | C2 | semidirect |
| 4. #20280660 | C2 | semidirect |
| 5. #20275926 | C2 | semidirect |
| 6. #20275695 | C2 | semidirect |
| 7. #20274927 | C2 | semidirect |
| 8. #20274528 | C2 | semidirect |
| 9. C53×#1965 | C2 | semidirect |
| 114. M16×C53 | #41 | semidirect |
| 201. #1965 | D53 | semidirect |
| 236. C53 | #25690 | semidirect |
| 314. M16 | #11719947 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20288589 | 2 |
| #20285267 | 2 |
| #20284538 | 2 |
| #20280660 | 2 |
| #20275926 | 2 |
| #20275695 | 2 |
| #20274927 | 2 |
| #20274528 | 2 |
| C53×#1965 | 2 |
| #25690 | 53 |