Finite Group DatabasebetaFinite Group DatabasebetaOrder 21376.
408 conjugacy classes of subgroups; only the 115 normal subgroups are shown.
This group has 408 conjugacy classes of subgroups — too many to draw. Only its 115 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. #24923984 | C2 | semidirect |
| 2. #24923939 | C2 | semidirect |
| 3. #24923615 | C2 | semidirect |
| 4. #24923591 | C2 | semidirect |
| 5. #24923565 | C2 | semidirect |
| 6. #24923502 | C2 | semidirect |
| 7. #24923411 | C2 | semidirect |
| 8. C4×#14581938 | C2 | semidirect |
| 9. #24923334 | C2 | semidirect |
| 10. #24923262 | C2 | semidirect |
| 11. #459×C167 | C2 | semidirect |
| 132. C167 | #3305 | semidirect |
| 140. #459 | D167 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #24923984 | 2 |
| #24923939 | 2 |
| #24923615 | 2 |
| #24923591 | 2 |
| #24923565 | 2 |
| #24923502 | 2 |
| #24923411 | 2 |
| C4×#14581938 | 2 |
| #24923334 | 2 |
| #24923262 | 2 |
| #459×C167 | 2 |
| #3305 | 167 |