Finite Group DatabasebetaFinite Group DatabasebetaOrder 21376.
700 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 700 conjugacy classes of subgroups — too many to draw. Only its 149 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. C2×#19128863 | C2 | semidirect |
| 3. #24923843 | C2 | semidirect |
| 4. #24923430 | C2 | semidirect |
| 5. #24923423 | C2 | semidirect |
| 6. #24923278 | C2 | semidirect |
| 7. #24923266 | C2 | semidirect |
| 8. #24923235 | C2 | semidirect |
| 9. C22×Q16×C167 | C2 | semidirect |
| 140. C167 | #3011 | semidirect |
| 144. C22×Q16 | D167 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19128880 | 2 |
| C2×#19128863 | 2 |
| #24923843 | 2 |
| #24923430 | 2 |
| #24923423 | 2 |
| #24923278 | 2 |
| #24923266 | 2 |
| #24923235 | 2 |
| C22×Q16×C167 | 2 |
| #3011 | 167 |