Finite Group DatabasebetaFinite Group DatabasebetaOrder 21376.
494 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 494 conjugacy classes of subgroups — too many to draw. Only its 133 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×#19128852 | C2 | semidirect |
| 2. #24923924 | C2 | semidirect |
| 3. #24923641 | C2 | semidirect |
| 4. #24923496 | C2 | semidirect |
| 5. #24923479 | C2 | semidirect |
| 6. #24923461 | C2 | semidirect |
| 7. #24923431 | C2 | semidirect |
| 8. #24923412 | C2 | semidirect |
| 9. C4×#14581937 | C2 | semidirect |
| 10. D4×C167⋊C8 | C2 | semidirect |
| 11. #550×C167 | C2 | semidirect |
| 52. #14581937 | D4 | semidirect |
| 129. C4×C167 | #135 | semidirect |
| 140. C167 | #3284 | semidirect |
| 143. #550 | D167 | semidirect |
| 272. C4 | #19128852 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19128852 | 2 |
| #24923924 | 2 |
| #24923641 | 2 |
| #24923496 | 2 |
| #24923479 | 2 |
| #24923461 | 2 |
| #24923431 | 2 |
| #24923412 | 2 |
| C4×#14581937 | 2 |
| D4×C167⋊C8 | 2 |
| #550×C167 | 2 |
| #3284 | 167 |