Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
472 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 472 conjugacy classes of subgroups — too many to draw. Only its 99 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. #20275703 | C2 | semidirect |
| 4. #20273397 | C2 | semidirect |
| 6. #20272604 | C2 | semidirect |
| 7. C53×#1309 | C2 | semidirect |
| 186. #1309 | D53 | semidirect |
| 216. C53 | #9353 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20284203 | 2 |
| #20283841 | 2 |
| #20275703 | 2 |
| #20273397 | 2 |
| #20273152 | 2 |
| #20272604 | 2 |
| C53×#1309 | 2 |
| #9353 | 53 |