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×#19128863 | C2 | semidirect |
| 2. C2×#19128839 | C2 | semidirect |
| 4. #24923525 | C2 | semidirect |
| 5. #24923517 | C2 | semidirect |
| 6. #24923508 | C2 | semidirect |
| 7. #24923500 | C2 | semidirect |
| 8. #24923312 | C2 | semidirect |
| 9. #24923263 | C2 | semidirect |
| 10. C2×#19128756 | C2 | semidirect |
| 11. #536×C167 | C2 | semidirect |
| 54. #14581934 | D4 | semidirect |
| 143. C167 | #3063 | semidirect |
| 148. #536 | D167 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19128863 | 2 |
| C2×#19128839 | 2 |
| #24923847 | 2 |
| #24923525 | 2 |
| #24923517 | 2 |
| #24923508 | 2 |
| #24923500 | 2 |
| #24923312 | 2 |
| #24923263 | 2 |
| C2×#19128756 | 2 |
| #536×C167 | 2 |
| #3063 | 167 |