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×#19128865 | C2 | semidirect |
| 2. D4×Dic334 | C2 | semidirect |
| 4. #24923649 | C2 | semidirect |
| 5. #24923527 | C2 | semidirect |
| 6. #24923480 | C2 | semidirect |
| 7. #24923475 | C2 | semidirect |
| 8. #24923433 | C2 | semidirect |
| 9. #24923427 | C2 | semidirect |
| 10. C4×#14581939 | C2 | semidirect |
| 11. #436×C167 | C2 | semidirect |
| 59. #14581939 | D4 | semidirect |
| 121. C4×C167 | #137 | semidirect |
| 134. C167 | #3276 | semidirect |
| 146. #436 | D167 | semidirect |
| 261. C4 | #19128865 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19128865 | 2 |
| D4×Dic334 | 2 |
| #24923924 | 2 |
| #24923649 | 2 |
| #24923527 | 2 |
| #24923480 | 2 |
| #24923475 | 2 |
| #24923433 | 2 |
| #24923427 | 2 |
| C4×#14581939 | 2 |
| #436×C167 | 2 |
| #3276 | 167 |