Finite Group DatabasebetaFinite Group DatabasebetaOrder 21376.
482 conjugacy classes of subgroups; only the 131 normal subgroups are shown.
This group has 482 conjugacy classes of subgroups — too many to draw. Only its 131 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. C2×#19128855 | C2 | semidirect |
| 2. C2×Q16×D167 | C2 | semidirect |
| 3. #24923931 | C2 | semidirect |
| 4. #24923653 | C2 | semidirect |
| 5. #24923511 | C2 | semidirect |
| 6. #24923506 | C2 | semidirect |
| 7. #24923491 | C2 | semidirect |
| 8. #24923434 | C2 | semidirect |
| 9. #24923409 | C2 | semidirect |
| 10. C8×D668 | C2 | semidirect |
| 11. C4×Q16×C167 | C2 | semidirect |
| 73. Q16×C167 | D4 | semidirect |
| 120. C2×D167 | #135 | semidirect |
| 136. C167 | #3285 | semidirect |
| 147. C4×Q16 | D167 | semidirect |
| 195. Q16 | D668 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19128855 | 2 |
| C2×Q16×D167 | 2 |
| #24923931 | 2 |
| #24923653 | 2 |
| #24923511 | 2 |
| #24923506 | 2 |
| #24923491 | 2 |
| #24923434 | 2 |
| #24923409 | 2 |
| C8×D668 | 2 |
| C4×Q16×C167 | 2 |
| #3285 | 167 |