Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
536 conjugacy classes of subgroups; only the 95 normal subgroups are shown.
This group has 536 conjugacy classes of subgroups — too many to draw. Only its 95 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. #20274703 | C2 | semidirect |
| 3. #20272716 | C2 | semidirect |
| 4. #20272713 | C2 | semidirect |
| 5. C53×#1459 | C2 | semidirect |
| 7. C2×C4×D212 | C4 | semidirect |
| 9. #16810548 | C4 | semidirect |
| 11. #16810532 | C4 | semidirect |
| 15. #16810489 | C4 | semidirect |
| 205. #1459 | D53 | semidirect |
| 234. C53 | #11875 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20279612 | 2 |
| #20274703 | 2 |
| #20272716 | 2 |
| #20272713 | 2 |
| C53×#1459 | 2 |
| #11875 | 53 |