Finite Group DatabasebetaFinite Group DatabasebetaOrder 21376.
380 conjugacy classes of subgroups; only the 69 normal subgroups are shown.
This group has 380 conjugacy classes of subgroups — too many to draw. Only its 69 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. #24924067 | C2 | semidirect |
| 2. C2×#19128860 | C2 | semidirect |
| 3. #24923833 | C2 | semidirect |
| 4. #24923273 | C2 | semidirect |
| 5. #24923242 | C2 | semidirect |
| 6. #24923041 | C2 | semidirect |
| 7. #421×C167 | C2 | semidirect |
| 36. C2×Dic334 | D4 | semidirect |
| 43. C2×D668 | D4 | semidirect |
| 55. C2×C167⋊C8 | D4 | semidirect |
| 70. M16×C167 | D4 | semidirect |
| 142. C167 | #2008 | semidirect |
| 147. #421 | D167 | semidirect |
| 208. M16 | C22⋊D167 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #24924067 | 2 |
| C2×#19128860 | 2 |
| #24923833 | 2 |
| #24923273 | 2 |
| #24923242 | 2 |
| #24923041 | 2 |
| #421×C167 | 2 |
| #2008 | 167 |