Finite Group DatabasebetaFinite Group DatabasebetaOrder 21376.
386 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 386 conjugacy classes of subgroups — too many to draw. Only its 125 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. #24923826 | C2 | semidirect |
| 3. #24923611 | C2 | semidirect |
| 4. #24923565 | C2 | semidirect |
| 5. #24923560 | C2 | semidirect |
| 6. #24923480 | C2 | semidirect |
| 7. #24923475 | C2 | semidirect |
| 9. #24923377 | C2 | semidirect |
| 10. #24923371 | C2 | semidirect |
| 11. #432×C167 | C2 | semidirect |
| 136. C167 | #3116 | semidirect |
| 148. #432 | D167 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #24923826 | 2 |
| C4×#14581950 | 2 |
| #24923611 | 2 |
| #24923565 | 2 |
| #24923560 | 2 |
| #24923480 | 2 |
| #24923475 | 2 |
| #24923433 | 2 |
| #24923377 | 2 |
| #24923371 | 2 |
| #432×C167 | 2 |
| #3116 | 167 |