Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
450 conjugacy classes of subgroups; only the 97 normal subgroups are shown.
This group has 450 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. #20283360 | C2 | semidirect |
| 3. #20273306 | C2 | semidirect |
| 4. #20273165 | C2 | semidirect |
| 5. #20273152 | C2 | semidirect |
| 6. #20272551 | C2 | semidirect |
| 7. C53×#1299 | C2 | semidirect |
| 201. #1299 | D53 | semidirect |
| 232. C53 | #9213 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20284776 | 2 |
| #20283360 | 2 |
| #20273306 | 2 |
| #20273165 | 2 |
| #20273152 | 2 |
| #20272551 | 2 |
| C53×#1299 | 2 |
| #9213 | 53 |