Finite Group DatabasebetaFinite Group DatabasebetaOrder 21376.
384 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 384 conjugacy classes of subgroups — too many to draw. Only its 123 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. #24924004 | C2 | semidirect |
| 2. Q8×D668 | C2 | semidirect |
| 3. #24923629 | C2 | semidirect |
| 4. #24923616 | C2 | semidirect |
| 5. #24923560 | C2 | semidirect |
| 6. #24923555 | C2 | semidirect |
| 7. #24923485 | C2 | semidirect |
| 9. #24923382 | C2 | semidirect |
| 10. C4×#14581939 | C2 | semidirect |
| 11. #446×C167 | C2 | semidirect |
| 124. C167 | #3373 | semidirect |
| 134. #446 | D167 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #24924004 | 2 |
| Q8×D668 | 2 |
| #24923629 | 2 |
| #24923616 | 2 |
| #24923560 | 2 |
| #24923555 | 2 |
| #24923485 | 2 |
| #24923465 | 2 |
| #24923382 | 2 |
| C4×#14581939 | 2 |
| #446×C167 | 2 |
| #3373 | 167 |