Finite Group DatabasebetaFinite Group DatabasebetaOrder 21376.
386 conjugacy classes of subgroups; only the 129 normal subgroups are shown.
This group has 386 conjugacy classes of subgroups — too many to draw. Only its 129 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. #24923604 | C2 | semidirect |
| 4. #24923576 | C2 | semidirect |
| 5. #24923491 | C2 | semidirect |
| 6. #24923425 | C2 | semidirect |
| 8. #24923374 | C2 | semidirect |
| 9. #24923367 | C2 | semidirect |
| 10. #24923326 | C2 | semidirect |
| 11. C2×C4×Q8×C167 | C2 | semidirect |
| 131. C167 | #3117 | semidirect |
| 134. C2×C4×Q8 | D167 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #24923803 | 2 |
| #24923604 | 2 |
| #24923587 | 2 |
| #24923576 | 2 |
| #24923491 | 2 |
| #24923425 | 2 |
| #24923408 | 2 |
| #24923374 | 2 |
| #24923367 | 2 |
| #24923326 | 2 |
| C2×C4×Q8×C167 | 2 |
| #3117 | 167 |