Finite Group DatabasebetaFinite Group DatabasebetaOrder 21376.
472 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 472 conjugacy classes of subgroups — too many to draw. Only its 149 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. C2×#19128865 | C2 | semidirect |
| 3. #24923840 | C2 | semidirect |
| 4. #24923527 | C2 | semidirect |
| 5. #24923515 | C2 | semidirect |
| 6. #24923510 | C2 | semidirect |
| 7. #24923498 | C2 | semidirect |
| 8. #24923311 | C2 | semidirect |
| 9. #24923266 | C2 | semidirect |
| 10. C2×#19128757 | C2 | semidirect |
| 11. C2×#131×C167 | C2 | semidirect |
| 79. M16×C167 | D4 | semidirect |
| 143. C167 | #3063 | semidirect |
| 146. C2×#131 | D167 | semidirect |
| 210. M16 | C22⋊D167 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19128865 | 2 |
| #24923847 | 2 |
| #24923840 | 2 |
| #24923527 | 2 |
| #24923515 | 2 |
| #24923510 | 2 |
| #24923498 | 2 |
| #24923311 | 2 |
| #24923266 | 2 |
| C2×#19128757 | 2 |
| C2×#131×C167 | 2 |
| #3063 | 167 |