Finite Group DatabasebetaFinite Group DatabasebetaOrder 21376.
420 conjugacy classes of subgroups; only the 139 normal subgroups are shown.
This group has 420 conjugacy classes of subgroups — too many to draw. Only its 139 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. D4×Dic334 | C2 | semidirect |
| 3. #24923620 | C2 | semidirect |
| 4. #24923600 | C2 | semidirect |
| 5. #24923555 | C2 | semidirect |
| 6. #24923498 | C2 | semidirect |
| 7. #24923475 | C2 | semidirect |
| 8. #24923410 | C2 | semidirect |
| 9. C4×#14581939 | C2 | semidirect |
| 10. C2×#19128757 | C2 | semidirect |
| 11. C8×D4×C167 | C2 | semidirect |
| 83. Dic334 | #41 | semidirect |
| 96. D4×C167 | SD16 | semidirect |
| 128. C167 | #3298 | semidirect |
| 139. C8×D4 | D167 | semidirect |
| 217. D4 | #14581939 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D4×Dic334 | 2 |
| #24923923 | 2 |
| #24923620 | 2 |
| #24923600 | 2 |
| #24923555 | 2 |
| #24923498 | 2 |
| #24923475 | 2 |
| #24923410 | 2 |
| C4×#14581939 | 2 |
| C2×#19128757 | 2 |
| C8×D4×C167 | 2 |
| #3298 | 167 |