Finite Group DatabasebetaFinite Group DatabasebetaOrder 21568.
234 conjugacy classes of subgroups; only the 101 normal subgroups are shown.
This group has 234 conjugacy classes of subgroups — too many to draw. Only its 101 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. #24924954 | C2 | semidirect |
| 2. #24924950 | C2 | semidirect |
| 3. #24924948 | C2 | semidirect |
| 4. #24924943 | C2 | semidirect |
| 6. Q8×Dic337 | C2 | semidirect |
| 7. #24924921 | C2 | semidirect |
| 8. #24924919 | C2 | semidirect |
| 9. #24924917 | C2 | semidirect |
| 10. C2×C4×Dic337 | C2 | semidirect |
| 11. C22⋊Q8×C337 | C2 | semidirect |
| 74. C337 | #529 | semidirect |
| 80. C22⋊Q8 | D337 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #24924954 | 2 |
| #24924950 | 2 |
| #24924948 | 2 |
| #24924943 | 2 |
| #24924933 | 2 |
| Q8×Dic337 | 2 |
| #24924921 | 2 |
| #24924919 | 2 |
| #24924917 | 2 |
| C2×C4×Dic337 | 2 |
| C22⋊Q8×C337 | 2 |
| #529 | 337 |