Finite Group DatabasebetaFinite Group DatabasebetaOrder 21376.
504 conjugacy classes of subgroups; only the 81 normal subgroups are shown.
This group has 504 conjugacy classes of subgroups — too many to draw. Only its 81 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. #24923036 | C2 | semidirect |
| 4. #24923035 | C2 | semidirect |
| 5. #342×C167 | C2 | semidirect |
| 7. C22×C4×D167 | C4 | semidirect |
| 11. C2×(C2×D167)⋊C4 | C4 | semidirect |
| 102. C167 | #1819 | semidirect |
| 108. #342 | D167 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C22⋊C4×D167 | 2 |
| #24923124 | 2 |
| #24923036 | 2 |
| #24923035 | 2 |
| #342×C167 | 2 |
| #1819 | 167 |