Finite Group DatabasebetaFinite Group DatabasebetaOrder 21376.
484 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 484 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×#19128852 | C2 | semidirect |
| 2. C2×#19128839 | C2 | semidirect |
| 3. #24923847 | C2 | semidirect |
| 4. #24923525 | C2 | semidirect |
| 5. #24923520 | C2 | semidirect |
| 6. #24923500 | C2 | semidirect |
| 7. #24923496 | C2 | semidirect |
| 8. C2×#19128763 | C2 | semidirect |
| 9. #24923270 | C2 | semidirect |
| 10. #24923268 | C2 | semidirect |
| 11. #537×C167 | C2 | semidirect |
| 58. C2×C167⋊C8 | D4 | semidirect |
| 152. C167 | #3060 | semidirect |
| 157. #537 | D167 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19128852 | 2 |
| C2×#19128839 | 2 |
| #24923847 | 2 |
| #24923525 | 2 |
| #24923520 | 2 |
| #24923500 | 2 |
| #24923496 | 2 |
| C2×#19128763 | 2 |
| #24923270 | 2 |
| #24923268 | 2 |
| #537×C167 | 2 |
| #3060 | 167 |