Finite Group DatabasebetaFinite Group DatabasebetaOrder 21376.
420 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 420 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. #24923597 | C2 | semidirect |
| 4. #24923554 | C2 | semidirect |
| 5. #24923500 | C2 | semidirect |
| 6. #24923471 | C2 | semidirect |
| 7. #24923408 | C2 | semidirect |
| 8. C4×#14581937 | C2 | semidirect |
| 9. D4×C167⋊C8 | C2 | semidirect |
| 10. C2×#19128756 | C2 | semidirect |
| 11. D4×Q8×C167 | C2 | semidirect |
| 94. Q8×C167 | #41 | semidirect |
| 95. D4×C167 | SD16 | semidirect |
| 128. C167 | #3298 | semidirect |
| 130. D4×Q8 | D167 | semidirect |
| 213. Q8 | #14581949 | semidirect |
| 217. D4 | #14581937 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #24923923 | 2 |
| #24923619 | 2 |
| #24923597 | 2 |
| #24923554 | 2 |
| #24923500 | 2 |
| #24923471 | 2 |
| #24923408 | 2 |
| C4×#14581937 | 2 |
| D4×C167⋊C8 | 2 |
| C2×#19128756 | 2 |
| D4×Q8×C167 | 2 |
| #3298 | 167 |