Finite Group DatabasebetaFinite Group DatabasebetaOrder 21376.
160 conjugacy classes of subgroups; only the 67 normal subgroups are shown.
This group has 160 conjugacy classes of subgroups — too many to draw. Only its 67 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 |
|---|---|---|
| 4. #24923022 | C2 | semidirect |
| 5. #24923021 | C2 | semidirect |
| 6. #24923019 | C2 | semidirect |
| 7. #334×C167 | C2 | semidirect |
| 75. C167 | #1573 | semidirect |
| 83. #334 | D167 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #24923325 | 2 |
| #24923320 | 2 |
| C4⋊C8×D167 | 2 |
| #24923022 | 2 |
| #24923021 | 2 |
| #24923019 | 2 |
| #334×C167 | 2 |
| #1573 | 167 |