Finite Group DatabasebetaFinite Group DatabasebetaOrder 21376.
492 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 492 conjugacy classes of subgroups — too many to draw. Only its 149 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. C22×#14581939 | C2 | semidirect |
| 2. #24923840 | C2 | semidirect |
| 4. #24923515 | C2 | semidirect |
| 5. #24923498 | C2 | semidirect |
| 6. #24923307 | C2 | semidirect |
| 7. #24923279 | C2 | semidirect |
| 8. #24923275 | C2 | semidirect |
| 9. C2×#131×C167 | C2 | semidirect |
| 20. #19128811 | C22 | semidirect |
| 25. #19128766 | C22 | semidirect |
| 26. #19128764 | C22 | semidirect |
| 27. #19128757 | C22 | semidirect |
| 32. C2×M16×C167 | C22 | semidirect |
| 34. C22×C8×C167 | C22 | semidirect |
| 67. C2×C8×C167 | D4 | semidirect |
| 120. C167 | #3057 | semidirect |
| 123. C2×#131 | D167 | semidirect |
| 139. C2×M16 | C2×D167 | semidirect |
| 141. C22×C8 | C2×D167 | semidirect |
| 179. C2×C8 | C22⋊D167 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#14581939 | 2 |
| #24923840 | 2 |
| #24923833 | 2 |
| #24923515 | 2 |
| #24923498 | 2 |
| #24923307 | 2 |
| #24923279 | 2 |
| #24923275 | 2 |
| C2×#131×C167 | 2 |
| #3057 | 167 |