Finite Group DatabasebetaFinite Group DatabasebetaOrder 21376.
380 conjugacy classes of subgroups; only the 121 normal subgroups are shown.
This group has 380 conjugacy classes of subgroups — too many to draw. Only its 121 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. #24923806 | C2 | semidirect |
| 2. #24923670 | C2 | semidirect |
| 3. #24923654 | C2 | semidirect |
| 4. #24923625 | C2 | semidirect |
| 5. #24923507 | C2 | semidirect |
| 7. #24923501 | C2 | semidirect |
| 8. C4×#14581937 | C2 | semidirect |
| 9. C4×D1336 | C2 | semidirect |
| 10. C4×C8×D167 | C2 | semidirect |
| 11. C4×Q16×C167 | C2 | semidirect |
| 118. C167 | #3168 | semidirect |
| 127. C4×Q16 | D167 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #24923806 | 2 |
| #24923670 | 2 |
| #24923654 | 2 |
| #24923625 | 2 |
| #24923507 | 2 |
| #24923506 | 2 |
| #24923501 | 2 |
| C4×#14581937 | 2 |
| C4×D1336 | 2 |
| C4×C8×D167 | 2 |
| C4×Q16×C167 | 2 |
| #3168 | 167 |