Finite Group DatabasebetaFinite Group DatabasebetaOrder 21376.
284 conjugacy classes of subgroups; only the 91 normal subgroups are shown.
This group has 284 conjugacy classes of subgroups — too many to draw. Only its 91 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 |
|---|---|---|
| 3. C2×#19128742 | C2 | semidirect |
| 5. #24923168 | C2 | semidirect |
| 6. #24923031 | C2 | semidirect |
| 7. #340×C167 | C2 | semidirect |
| 16. #19128752 | C4 | semidirect |
| 118. C167 | #1936 | semidirect |
| 126. #340 | D167 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19128754 | 2 |
| C2×#19128752 | 2 |
| C2×#19128742 | 2 |
| #24923170 | 2 |
| #24923168 | 2 |
| #24923031 | 2 |
| #340×C167 | 2 |
| #1936 | 167 |