Finite Group DatabasebetaFinite Group DatabasebetaOrder 21376.
484 conjugacy classes of subgroups; only the 131 normal subgroups are shown.
This group has 484 conjugacy classes of subgroups — too many to draw. Only its 131 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×#19128861 | C2 | semidirect |
| 3. C4×Q8×D167 | C2 | semidirect |
| 4. #24923490 | C2 | semidirect |
| 5. #24923489 | C2 | semidirect |
| 6. #24923480 | C2 | semidirect |
| 7. #24923479 | C2 | semidirect |
| 8. #24923466 | C2 | semidirect |
| 9. #24923291 | C2 | semidirect |
| 10. #24923267 | C2 | semidirect |
| 11. #460×C167 | C2 | semidirect |
| 50. Q8×D167 | D4 | semidirect |
| 132. C4×C167 | #137 | semidirect |
| 146. C167 | #3037 | semidirect |
| 156. #460 | D167 | semidirect |
| 285. C4 | #19128861 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19128861 | 2 |
| #24923817 | 2 |
| C4×Q8×D167 | 2 |
| #24923490 | 2 |
| #24923489 | 2 |
| #24923480 | 2 |
| #24923479 | 2 |
| #24923466 | 2 |
| #24923291 | 2 |
| #24923267 | 2 |
| #460×C167 | 2 |
| #3037 | 167 |