Finite Group DatabasebetaFinite Group DatabasebetaOrder 21376.
398 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 398 conjugacy classes of subgroups — too many to draw. Only its 117 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. #24923923 | C2 | semidirect |
| 3. #24923620 | C2 | semidirect |
| 4. #24923612 | C2 | semidirect |
| 5. #24923559 | C2 | semidirect |
| 6. #24923497 | C2 | semidirect |
| 7. #24923474 | C2 | semidirect |
| 8. #24923411 | C2 | semidirect |
| 9. C8×D668 | C2 | semidirect |
| 10. #24923262 | C2 | semidirect |
| 11. C4×D8×C167 | C2 | semidirect |
| 130. C167 | #3303 | semidirect |
| 140. C4×D8 | D167 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #24923984 | 2 |
| #24923923 | 2 |
| #24923620 | 2 |
| #24923612 | 2 |
| #24923559 | 2 |
| #24923497 | 2 |
| #24923474 | 2 |
| #24923411 | 2 |
| C8×D668 | 2 |
| #24923262 | 2 |
| C4×D8×C167 | 2 |
| #3303 | 167 |