Finite Group DatabasebetaFinite Group DatabasebetaOrder 21376.
372 conjugacy classes of subgroups; only the 115 normal subgroups are shown.
This group has 372 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 |
|---|---|---|
| 1. #24924004 | C2 | semidirect |
| 2. #24923993 | C2 | semidirect |
| 3. #24923654 | C2 | semidirect |
| 4. #24923643 | C2 | semidirect |
| 5. #24923493 | C2 | semidirect |
| 6. #24923487 | C2 | semidirect |
| 8. #24923393 | C2 | semidirect |
| 9. C4×#14581937 | C2 | semidirect |
| 10. #24923354 | C2 | semidirect |
| 11. #462×C167 | C2 | semidirect |
| 125. C167 | #3394 | semidirect |
| 133. #462 | D167 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #24924004 | 2 |
| #24923993 | 2 |
| #24923654 | 2 |
| #24923643 | 2 |
| #24923493 | 2 |
| #24923487 | 2 |
| #24923465 | 2 |
| #24923393 | 2 |
| C4×#14581937 | 2 |
| #24923354 | 2 |
| #462×C167 | 2 |
| #3394 | 167 |