Finite Group DatabasebetaFinite Group DatabasebetaOrder 21376.
496 conjugacy classes of subgroups; only the 131 normal subgroups are shown.
This group has 496 conjugacy classes of subgroups — too many to draw. Only its 131 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×#19128853 | C2 | semidirect |
| 2. #24923820 | C2 | semidirect |
| 3. C4×#14581949 | C2 | semidirect |
| 4. #24923494 | C2 | semidirect |
| 5. #24923486 | C2 | semidirect |
| 6. #24923476 | C2 | semidirect |
| 7. #24923470 | C2 | semidirect |
| 8. #24923464 | C2 | semidirect |
| 9. C4⋊C8×D167 | C2 | semidirect |
| 10. #24923264 | C2 | semidirect |
| 11. #461×C167 | C2 | semidirect |
| 47. #14581949 | D4 | semidirect |
| 136. C4×C167 | #135 | semidirect |
| 150. C167 | #3035 | semidirect |
| 158. #461 | D167 | semidirect |
| 292. C4 | #19128853 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19128853 | 2 |
| #24923820 | 2 |
| C4×#14581949 | 2 |
| #24923494 | 2 |
| #24923486 | 2 |
| #24923476 | 2 |
| #24923470 | 2 |
| #24923464 | 2 |
| C4⋊C8×D167 | 2 |
| #24923264 | 2 |
| #461×C167 | 2 |
| #3035 | 167 |