Finite Group DatabasebetaFinite Group DatabasebetaOrder 21376.
472 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 472 conjugacy classes of subgroups — too many to draw. Only its 133 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×#19128838 | C2 | semidirect |
| 4. #24923843 | C2 | semidirect |
| 5. #24923526 | C2 | semidirect |
| 6. #24923518 | C2 | semidirect |
| 7. #24923509 | C2 | semidirect |
| 8. #24923501 | C2 | semidirect |
| 9. #24923309 | C2 | semidirect |
| 10. #24923266 | C2 | semidirect |
| 11. C2×#103×C167 | C2 | semidirect |
| 58. #14581934 | D4 | semidirect |
| 143. C167 | #3063 | semidirect |
| 155. C2×#103 | 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×#19128838 | 2 |
| #24923850 | 2 |
| #24923843 | 2 |
| #24923526 | 2 |
| #24923518 | 2 |
| #24923509 | 2 |
| #24923501 | 2 |
| #24923309 | 2 |
| #24923266 | 2 |
| C2×#103×C167 | 2 |
| #3063 | 167 |