Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
810 conjugacy classes of subgroups; only the 176 normal subgroups are shown.
This group has 810 conjugacy classes of subgroups — too many to draw. Only its 176 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 |
|---|---|---|
| 1. #20291444 | C2 | semidirect |
| 2. #20291442 | C2 | semidirect |
| 3. #20290853 | C2 | semidirect |
| 4. #20290851 | C2 | semidirect |
| 5. #20290707 | C2 | semidirect |
| 6. #20290704 | C2 | semidirect |
| 7. #20290640 | C2 | semidirect |
| 8. #20290433 | C2 | semidirect |
| 28. #16811004 | C4 | semidirect |
| 29. #16811002 | C4 | semidirect |
| 30. #16810999 | C4 | semidirect |
| 31. #16810996 | C4 | semidirect |
| 33. C53×#492 | C4 | semidirect |
| 193. #492 | #6157 | semidirect |
| 208. C53 | #22282 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20291444 | 2 |
| #20291442 | 2 |
| #20290853 | 2 |
| #20290851 | 2 |
| #20290707 | 2 |
| #20290704 | 2 |
| #20290640 | 2 |
| #20290433 | 2 |
| #20285138 | 2 |
| #22282 | 53 |