Finite Group DatabasebetaFinite Group DatabasebetaOrder 21568.
234 conjugacy classes of subgroups; only the 103 normal subgroups are shown.
This group has 234 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 |
|---|---|---|
| 1. #24924953 | C2 | semidirect |
| 2. #24924951 | C2 | semidirect |
| 3. #24924947 | C2 | semidirect |
| 4. #24924942 | C2 | semidirect |
| 5. #24924938 | C2 | semidirect |
| 7. C4×Dic674 | C2 | semidirect |
| 8. C4×D1348 | C2 | semidirect |
| 9. C4×C22⋊D337 | C2 | semidirect |
| 10. #24924916 | C2 | semidirect |
| 11. C2×C42×C337 | C2 | semidirect |
| 74. C337 | #529 | semidirect |
| 86. C2×C42 | D337 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #24924953 | 2 |
| #24924951 | 2 |
| #24924947 | 2 |
| #24924942 | 2 |
| #24924938 | 2 |
| #24924933 | 2 |
| C4×Dic674 | 2 |
| C4×D1348 | 2 |
| C4×C22⋊D337 | 2 |
| #24924916 | 2 |
| C2×C42×C337 | 2 |
| #529 | 337 |