Finite Group DatabasebetaFinite Group DatabasebetaOrder 21376.
170 conjugacy classes of subgroups; only the 49 normal subgroups are shown.
This group has 170 conjugacy classes of subgroups — too many to draw. Only its 49 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. #24923615 | C2 | semidirect |
| 2. #24923560 | C2 | semidirect |
| 4. #24923346 | C2 | semidirect |
| 5. #24923021 | C2 | semidirect |
| 6. #24923017 | C2 | semidirect |
| 7. #331×C167 | C2 | semidirect |
| 82. C167 | #1697 | semidirect |
| 90. #331 | D167 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #24923615 | 2 |
| #24923560 | 2 |
| #24923461 | 2 |
| #24923346 | 2 |
| #24923021 | 2 |
| #24923017 | 2 |
| #331×C167 | 2 |
| #1697 | 167 |