Finite Group DatabasebetaFinite Group DatabasebetaOrder 21376.
418 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 418 conjugacy classes of subgroups — too many to draw. Only its 123 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. #24924004 | C2 | semidirect |
| 2. #24923656 | C2 | semidirect |
| 3. #24923645 | C2 | semidirect |
| 4. #24923484 | C2 | semidirect |
| 5. #24923466 | C2 | semidirect |
| 6. #24923464 | C2 | semidirect |
| 7. #24923461 | C2 | semidirect |
| 8. #24923400 | C2 | semidirect |
| 9. #24923379 | C2 | semidirect |
| 10. C4×#14581938 | C2 | semidirect |
| 11. #550×C167 | C2 | semidirect |
| 89. C167⋊C8 | #41 | semidirect |
| 134. C167 | #3399 | semidirect |
| 137. #550 | D167 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #24924004 | 2 |
| #24923656 | 2 |
| #24923645 | 2 |
| #24923484 | 2 |
| #24923466 | 2 |
| #24923464 | 2 |
| #24923461 | 2 |
| #24923400 | 2 |
| #24923379 | 2 |
| C4×#14581938 | 2 |
| #550×C167 | 2 |
| #3399 | 167 |