Finite Group DatabasebetaFinite Group DatabasebetaOrder 21376.
384 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 384 conjugacy classes of subgroups — too many to draw. Only its 117 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. #24924004 | C2 | semidirect |
| 2. D4×Dic334 | C2 | semidirect |
| 3. #24923630 | C2 | semidirect |
| 4. #24923616 | C2 | semidirect |
| 5. #24923558 | C2 | semidirect |
| 6. #24923554 | C2 | semidirect |
| 7. #24923486 | C2 | semidirect |
| 9. #24923399 | C2 | semidirect |
| 10. #24923378 | C2 | semidirect |
| 11. C4×SD16×C167 | C2 | semidirect |
| 124. C167 | #3373 | semidirect |
| 136. C4×SD16 | D167 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #24924004 | 2 |
| D4×Dic334 | 2 |
| #24923630 | 2 |
| #24923616 | 2 |
| #24923558 | 2 |
| #24923554 | 2 |
| #24923486 | 2 |
| #24923464 | 2 |
| #24923399 | 2 |
| #24923378 | 2 |
| C4×SD16×C167 | 2 |
| #3373 | 167 |