Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
490 conjugacy classes of subgroups; only the 77 normal subgroups are shown.
This group has 490 conjugacy classes of subgroups — too many to draw. Only its 77 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. #20275153 | C2 | semidirect |
| 3. #20274920 | C2 | semidirect |
| 4. #20273283 | C2 | semidirect |
| 5. #20273076 | C2 | semidirect |
| 6. #20272622 | C2 | semidirect |
| 7. C53×#1900 | C2 | semidirect |
| 217. #1900 | D53 | semidirect |
| 253. C53 | #10560 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20285512 | 2 |
| #20275153 | 2 |
| #20274920 | 2 |
| #20273283 | 2 |
| #20273076 | 2 |
| #20272622 | 2 |
| C53×#1900 | 2 |
| #10560 | 53 |