Finite Group DatabasebetaFinite Group DatabasebetaOrder 21376.
326 conjugacy classes of subgroups; only the 87 normal subgroups are shown.
This group has 326 conjugacy classes of subgroups — too many to draw. Only its 87 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×#19128831 | C2 | semidirect |
| 5. #24923031 | C2 | semidirect |
| 6. #24923023 | C2 | semidirect |
| 7. #340×C167 | C2 | semidirect |
| 32. C2×D668 | Q8 | semidirect |
| 123. C167 | #2023 | semidirect |
| 130. #340 | D167 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19128831 | 2 |
| C2×#19128754 | 2 |
| C2×#19128752 | 2 |
| #24923170 | 2 |
| #24923031 | 2 |
| #24923023 | 2 |
| #340×C167 | 2 |
| #2023 | 167 |