Finite Group DatabasebetaFinite Group DatabasebetaOrder 21376.
260 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 260 conjugacy classes of subgroups — too many to draw. Only its 89 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. #24923307 | C2 | semidirect |
| 4. #24923025 | C2 | semidirect |
| 5. #427×C167 | C2 | semidirect |
| 12. C2×#14581933 | C4 | semidirect |
| 13. C2×C8×D167 | C4 | semidirect |
| 92. C167 | #1812 | semidirect |
| 96. #427 | D167 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19128838 | 2 |
| #24923307 | 2 |
| #24923242 | 2 |
| #24923025 | 2 |
| #427×C167 | 2 |
| #1812 | 167 |