Finite Group DatabasebetaFinite Group DatabasebetaOrder 21376.
738 conjugacy classes of subgroups; only the 173 normal subgroups are shown.
This group has 738 conjugacy classes of subgroups — too many to draw. Only its 173 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. C2×#19128863 | C2 | semidirect |
| 3. #24923425 | C2 | semidirect |
| 4. #24923408 | C2 | semidirect |
| 5. #24923278 | C2 | semidirect |
| 6. #24923233 | C2 | semidirect |
| 7. C23×Q8×C167 | C2 | semidirect |
| 10. C2×#14581940 | C22 | semidirect |
| 11. C2×#14581937 | C22 | semidirect |
| 19. #19128756 | C22 | semidirect |
| 51. C2×Q8×C167 | D4 | semidirect |
| 93. C22×C167 | #137 | semidirect |
| 108. C167 | #3004 | semidirect |
| 110. C23×Q8 | D167 | semidirect |
| 146. C2×Q8 | C22⋊D167 | semidirect |
| 204. C22 | #19128863 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19128863 | 2 |
| #24923780 | 2 |
| #24923425 | 2 |
| #24923408 | 2 |
| #24923278 | 2 |
| #24923233 | 2 |
| C23×Q8×C167 | 2 |
| #3004 | 167 |