Finite Group DatabasebetaFinite Group DatabasebetaOrder 21376.
472 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 472 conjugacy classes of subgroups — too many to draw. Only its 141 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×#19128840 | C2 | semidirect |
| 3. #24923843 | C2 | semidirect |
| 4. #24923524 | C2 | semidirect |
| 5. #24923512 | C2 | semidirect |
| 6. #24923507 | C2 | semidirect |
| 7. #24923495 | C2 | semidirect |
| 8. #24923311 | C2 | semidirect |
| 9. #24923265 | C2 | semidirect |
| 10. C2×#19128756 | C2 | semidirect |
| 11. C2×#137×C167 | C2 | semidirect |
| 83. M16×C167 | D4 | semidirect |
| 143. C167 | #3063 | semidirect |
| 145. C2×#137 | 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×#19128840 | 2 |
| #24923847 | 2 |
| #24923843 | 2 |
| #24923524 | 2 |
| #24923512 | 2 |
| #24923507 | 2 |
| #24923495 | 2 |
| #24923311 | 2 |
| #24923265 | 2 |
| C2×#19128756 | 2 |
| C2×#137×C167 | 2 |
| #3063 | 167 |