Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
690 conjugacy classes of subgroups; only the 105 normal subgroups are shown.
This group has 690 conjugacy classes of subgroups — too many to draw. Only its 105 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. #20277312 | C2 | semidirect |
| 3. #20273283 | C2 | semidirect |
| 4. C2×#16810346 | C2 | semidirect |
| 5. #20272583 | C2 | semidirect |
| 6. #20272582 | C2 | semidirect |
| 7. C53×#1519 | C2 | semidirect |
| 11. #16810549 | C4 | semidirect |
| 13. #16810531 | C4 | semidirect |
| 53. #13133124 | D4 | semidirect |
| 68. #95×C53 | D4 | semidirect |
| 243. #1519 | D53 | semidirect |
| 277. C53 | #9205 | semidirect |
| 319. #95 | C22⋊D53 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20280451 | 2 |
| #20277312 | 2 |
| #20273283 | 2 |
| C2×#16810346 | 2 |
| #20272583 | 2 |
| #20272582 | 2 |
| C53×#1519 | 2 |
| #9205 | 53 |