Finite Group DatabasebetaFinite Group DatabasebetaOrder 21376.
382 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 382 conjugacy classes of subgroups — too many to draw. Only its 125 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. #24923635 | C2 | semidirect |
| 3. #24923617 | C2 | semidirect |
| 4. #24923566 | C2 | semidirect |
| 5. #24923546 | C2 | semidirect |
| 6. #24923469 | C2 | semidirect |
| 7. #24923469 | C2 | semidirect |
| 8. #24923400 | C2 | semidirect |
| 9. #24923367 | C2 | semidirect |
| 10. C4×#14581937 | C2 | semidirect |
| 11. #557×C167 | C2 | semidirect |
| 93. Q8×C167 | #41 | semidirect |
| 124. C167 | #3368 | semidirect |
| 126. #557 | D167 | semidirect |
| 204. Q8 | #14581951 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #24923941 | 2 |
| #24923635 | 2 |
| #24923617 | 2 |
| #24923566 | 2 |
| #24923546 | 2 |
| #24923469 | 2 |
| #24923400 | 2 |
| #24923367 | 2 |
| C4×#14581937 | 2 |
| #557×C167 | 2 |
| #3368 | 167 |