Finite Group DatabasebetaFinite Group DatabasebetaOrder 21376.
336 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 336 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. #24923997 | C2 | semidirect |
| 4. #24923620 | C2 | semidirect |
| 5. #24923577 | C2 | semidirect |
| 8. #24923480 | C2 | semidirect |
| 9. C4×Dic668 | C2 | semidirect |
| 11. C8×Q8×C167 | C2 | semidirect |
| 115. C167 | #3364 | semidirect |
| 125. C8×Q8 | D167 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #24923997 | 2 |
| #24923992 | 2 |
| #24923624 | 2 |
| #24923620 | 2 |
| #24923577 | 2 |
| #24923550 | 2 |
| #24923492 | 2 |
| #24923480 | 2 |
| C4×Dic668 | 2 |
| C4×#14581939 | 2 |
| C8×Q8×C167 | 2 |
| #3364 | 167 |