Finite Group DatabasebetaFinite Group DatabasebetaOrder 21376.
388 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 388 conjugacy classes of subgroups — too many to draw. Only its 141 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. #24923619 | C2 | semidirect |
| 3. #24923602 | C2 | semidirect |
| 4. #24923564 | C2 | semidirect |
| 5. #24923508 | C2 | semidirect |
| 6. #24923476 | C2 | semidirect |
| 7. #24923425 | C2 | semidirect |
| 8. C4×#14581940 | C2 | semidirect |
| 10. C2×#19128756 | C2 | semidirect |
| 92. D4×C167 | Q16 | semidirect |
| 122. C167 | #3299 | semidirect |
| 208. D4 | #14581940 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #24923976 | 2 |
| #24923619 | 2 |
| #24923602 | 2 |
| #24923564 | 2 |
| #24923508 | 2 |
| #24923476 | 2 |
| #24923425 | 2 |
| C4×#14581940 | 2 |
| D4×C167⋊C8 | 2 |
| C2×#19128756 | 2 |
| D4×Q8×C167 | 2 |
| #3299 | 167 |