Finite Group DatabasebetaFinite Group DatabasebetaOrder 21376.
424 conjugacy classes of subgroups; only the 121 normal subgroups are shown.
This group has 424 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 |
|---|---|---|
| 2. C4×Q8×D167 | C2 | semidirect |
| 3. #24923581 | C2 | semidirect |
| 4. #24923565 | C2 | semidirect |
| 5. #24923564 | C2 | semidirect |
| 6. #24923466 | C2 | semidirect |
| 7. #24923406 | C2 | semidirect |
| 8. #24923370 | C2 | semidirect |
| 9. #24923366 | C2 | semidirect |
| 10. #24923325 | C2 | semidirect |
| 11. #460×C167 | C2 | semidirect |
| 87. Dic334 | #41 | semidirect |
| 105. Q8×C167 | #41 | semidirect |
| 140. C167 | #3112 | semidirect |
| 148. #460 | D167 | semidirect |
| 231. Q8 | #14581949 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #24923817 | 2 |
| C4×Q8×D167 | 2 |
| #24923581 | 2 |
| #24923565 | 2 |
| #24923564 | 2 |
| #24923466 | 2 |
| #24923406 | 2 |
| #24923370 | 2 |
| #24923366 | 2 |
| #24923325 | 2 |
| #460×C167 | 2 |
| #3112 | 167 |