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 |
| 3. #24923619 | C2 | semidirect |
| 5. #24923554 | C2 | semidirect |
| 7. #24923476 | C2 | semidirect |
| 8. #24923400 | C2 | semidirect |
| 9. #24923374 | C2 | semidirect |
| 116. C167 | #3369 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| Q8×Dic334 | 2 |
| #24923628 | 2 |
| #24923619 | 2 |
| #24923559 | 2 |
| #24923554 | 2 |
| #24923488 | 2 |
| #24923476 | 2 |
| #24923400 | 2 |
| #24923374 | 2 |
| C4×#14581938 | 2 |
| #556×C167 | 2 |
| #3369 | 167 |