Finite Group DatabasebetaFinite Group DatabasebetaOrder 21376.
398 conjugacy classes of subgroups; only the 115 normal subgroups are shown.
This group has 398 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. #24923922 | C2 | semidirect |
| 3. #24923619 | C2 | semidirect |
| 4. #24923608 | C2 | semidirect |
| 5. #24923560 | C2 | semidirect |
| 6. #24923495 | C2 | semidirect |
| 7. #24923413 | C2 | semidirect |
| 8. C4×#14581935 | C2 | semidirect |
| 9. #24923334 | C2 | semidirect |
| 10. #24923264 | C2 | semidirect |
| 11. #461×C167 | C2 | semidirect |
| 130. C167 | #3303 | semidirect |
| 138. #461 | D167 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #24923984 | 2 |
| #24923922 | 2 |
| #24923619 | 2 |
| #24923608 | 2 |
| #24923560 | 2 |
| #24923495 | 2 |
| #24923413 | 2 |
| C4×#14581935 | 2 |
| #24923334 | 2 |
| #24923264 | 2 |
| #461×C167 | 2 |
| #3303 | 167 |