Finite Group DatabasebetaFinite Group DatabasebetaOrder 21376.
338 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 338 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. Q8×Dic334 | C2 | semidirect |
| 4. #24923620 | C2 | semidirect |
| 6. #24923555 | C2 | semidirect |
| 8. #24923480 | C2 | semidirect |
| 9. #24923377 | C2 | semidirect |
| 11. #446×C167 | C2 | semidirect |
| 116. C167 | #3369 | semidirect |
| 126. #446 | D167 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| Q8×Dic334 | 2 |
| #24923992 | 2 |
| #24923629 | 2 |
| #24923620 | 2 |
| #24923560 | 2 |
| #24923555 | 2 |
| #24923492 | 2 |
| #24923480 | 2 |
| #24923377 | 2 |
| C4×#14581939 | 2 |
| #446×C167 | 2 |
| #3369 | 167 |