Finite Group DatabasebetaFinite Group DatabasebetaOrder 21376.
272 conjugacy classes of subgroups; only the 73 normal subgroups are shown.
This group has 272 conjugacy classes of subgroups — too many to draw. Only its 73 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. #24923115 | C2 | semidirect |
| 3. #24923004 | C2 | semidirect |
| 4. #432×C167 | C2 | semidirect |
| 6. #19128832 | C4 | semidirect |
| 7. #19128829 | C4 | semidirect |
| 12. C4×D668 | C4 | semidirect |
| 83. C167 | #1505 | semidirect |
| 86. #432 | D167 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #24923819 | 2 |
| #24923115 | 2 |
| #24923004 | 2 |
| #432×C167 | 2 |
| #1505 | 167 |