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 |
|---|---|---|
| 1. #24923891 | C2 | semidirect |
| 2. #24923666 | C2 | semidirect |
| 3. #24923654 | C2 | semidirect |
| 4. #24923630 | C2 | semidirect |
| 5. #24923524 | C2 | semidirect |
| 7. #24923501 | C2 | semidirect |
| 8. #24923382 | C2 | semidirect |
| 9. C4×#14581937 | C2 | semidirect |
| 10. #24923226 | C2 | semidirect |
| 11. #441×C167 | C2 | semidirect |
| 109. C167 | #3173 | semidirect |
| 119. #441 | D167 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #24923891 | 2 |
| #24923666 | 2 |
| #24923654 | 2 |
| #24923630 | 2 |
| #24923524 | 2 |
| #24923523 | 2 |
| #24923501 | 2 |
| #24923382 | 2 |
| C4×#14581937 | 2 |
| #24923226 | 2 |
| #441×C167 | 2 |
| #3173 | 167 |