Finite Group DatabasebetaFinite Group DatabasebetaOrder 21376.
372 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 372 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. #24923989 | C2 | semidirect |
| 3. #24923650 | C2 | semidirect |
| 4. #24923642 | C2 | semidirect |
| 5. #24923494 | C2 | semidirect |
| 6. #24923483 | C2 | semidirect |
| 7. #24923479 | C2 | semidirect |
| 9. C8×Dic334 | C2 | semidirect |
| 10. #24923356 | C2 | semidirect |
| 11. C4×SD16×C167 | C2 | semidirect |
| 125. C167 | #3394 | semidirect |
| 137. 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 |
| #24923989 | 2 |
| #24923650 | 2 |
| #24923642 | 2 |
| #24923494 | 2 |
| #24923483 | 2 |
| #24923479 | 2 |
| #24923464 | 2 |
| C8×Dic334 | 2 |
| #24923356 | 2 |
| C4×SD16×C167 | 2 |
| #3394 | 167 |