Finite Group DatabasebetaFinite Group DatabasebetaOrder 21376.
338 conjugacy classes of subgroups; only the 115 normal subgroups are shown.
This group has 338 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. #24923999 | C2 | semidirect |
| 4. #24923621 | C2 | semidirect |
| 5. #24923553 | C2 | semidirect |
| 7. #24923480 | C2 | semidirect |
| 8. #24923396 | C2 | semidirect |
| 9. #24923375 | C2 | semidirect |
| 116. C167 | #3369 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #24923999 | 2 |
| #24923989 | 2 |
| #24923627 | 2 |
| #24923621 | 2 |
| #24923553 | 2 |
| #24923490 | 2 |
| #24923480 | 2 |
| #24923396 | 2 |
| #24923375 | 2 |
| C4×#14581938 | 2 |
| #476×C167 | 2 |
| #3369 | 167 |