Finite Group DatabasebetaFinite Group DatabasebetaOrder 21376.
456 conjugacy classes of subgroups; only the 173 normal subgroups are shown.
This group has 456 conjugacy classes of subgroups — too many to draw. Only its 173 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. #24923164 | C2 | semidirect |
| 4. #24923150 | C2 | semidirect |
| 6. #24923137 | C2 | semidirect |
| 7. #384×C167 | C2 | semidirect |
| 9. #19128826 | C4 | semidirect |
| 28. Dic167⋊C4 | C2×C4 | semidirect |
| 37. C42×C167 | C2×C4 | semidirect |
| 72. C167 | #2383 | semidirect |
| 79. #384 | D167 | semidirect |
| 110. C42 | C4×D167 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19128826 | 2 |
| #24923164 | 2 |
| #24923159 | 2 |
| #24923150 | 2 |
| #24923140 | 2 |
| #24923137 | 2 |
| #384×C167 | 2 |
| #2383 | 167 |