Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
672 conjugacy classes of subgroups; only the 103 normal subgroups are shown.
This group has 672 conjugacy classes of subgroups — too many to draw. Only its 103 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. #20273420 | C2 | semidirect |
| 3. #20273344 | C2 | semidirect |
| 4. #20273290 | C2 | semidirect |
| 5. #20273265 | C2 | semidirect |
| 6. #20273187 | C2 | semidirect |
| 7. C53×#1514 | C2 | semidirect |
| 9. #16811338 | C4 | semidirect |
| 11. #16811330 | C4 | semidirect |
| 14. D4×Dic106 | C4 | semidirect |
| 16. #16811278 | C4 | semidirect |
| 268. #1514 | D53 | semidirect |
| 308. C53 | #8502 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20289104 | 2 |
| #20273420 | 2 |
| #20273344 | 2 |
| #20273290 | 2 |
| #20273265 | 2 |
| #20273187 | 2 |
| C53×#1514 | 2 |
| #8502 | 53 |