Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
538 conjugacy classes of subgroups; only the 97 normal subgroups are shown.
This group has 538 conjugacy classes of subgroups — too many to draw. Only its 97 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. #20274782 | C2 | semidirect |
| 3. #20274472 | C2 | semidirect |
| 4. #20272541 | C2 | semidirect |
| 5. #20272535 | C2 | semidirect |
| 6. #20272535 | C2 | semidirect |
| 7. C53×#1272 | C2 | semidirect |
| 220. #1272 | D53 | semidirect |
| 251. C53 | #7670 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20283019 | 2 |
| #20274782 | 2 |
| #20274472 | 2 |
| #20272541 | 2 |
| #20272535 | 2 |
| C53×#1272 | 2 |
| #7670 | 53 |