Finite Group DatabasebetaFinite Group DatabasebetaOrder 21376.
396 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 396 conjugacy classes of subgroups — too many to draw. Only its 117 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. #24923976 | C2 | semidirect |
| 2. #24923939 | C2 | semidirect |
| 3. #24923632 | C2 | semidirect |
| 4. #24923615 | C2 | semidirect |
| 5. #24923571 | C2 | semidirect |
| 6. #24923560 | C2 | semidirect |
| 7. #24923462 | C2 | semidirect |
| 8. #24923396 | C2 | semidirect |
| 9. #24923381 | C2 | semidirect |
| 10. C4×#14581935 | C2 | semidirect |
| 11. #459×C167 | C2 | semidirect |
| 97. D4×C167 | #41 | semidirect |
| 129. C167 | #3366 | semidirect |
| 138. #459 | D167 | semidirect |
| 218. D4 | #14581949 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #24923976 | 2 |
| #24923939 | 2 |
| #24923632 | 2 |
| #24923615 | 2 |
| #24923571 | 2 |
| #24923560 | 2 |
| #24923462 | 2 |
| #24923396 | 2 |
| #24923381 | 2 |
| C4×#14581935 | 2 |
| #459×C167 | 2 |
| #3366 | 167 |