Finite Group DatabasebetaFinite Group DatabasebetaOrder 21376.
362 conjugacy classes of subgroups; only the 115 normal subgroups are shown.
This group has 362 conjugacy classes of subgroups — too many to draw. Only its 115 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. #24923994 | C2 | semidirect |
| 3. #24923662 | C2 | semidirect |
| 5. #24923493 | C2 | semidirect |
| 6. #24923473 | C2 | semidirect |
| 8. #24923396 | C2 | semidirect |
| 9. #24923372 | C2 | semidirect |
| 10. C4×#14581940 | C2 | semidirect |
| 11. #462×C167 | C2 | semidirect |
| 121. C167 | #3400 | semidirect |
| 128. #462 | D167 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #24924004 | 2 |
| #24923994 | 2 |
| #24923662 | 2 |
| #24923643 | 2 |
| #24923493 | 2 |
| #24923473 | 2 |
| #24923470 | 2 |
| #24923396 | 2 |
| #24923372 | 2 |
| C4×#14581940 | 2 |
| #462×C167 | 2 |
| #3400 | 167 |