Finite Group DatabasebetaFinite Group DatabasebetaOrder 1408.
398 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 398 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 |
|---|---|---|
| 2. #10623050 | C2 | semidirect |
| 5. #10622622 | C2 | semidirect |
| 6. #10622622 | C2 | semidirect |
| 7. #10622621 | C2 | semidirect |
| 8. #10622620 | C2 | semidirect |
| 9. #10622612 | C2 | semidirect |
| 10. #10622611 | C2 | semidirect |
| 11. #10622608 | C2 | semidirect |
| 27. #66923 | C22 | semidirect |
| 28. #66922 | C22 | semidirect |
| 33. #66872 | C22 | semidirect |
| 34. #66872 | C22 | semidirect |
| 35. #66872 | C22 | semidirect |
| 36. #66871 | C22 | semidirect |
| 37. #66871 | C22 | semidirect |
| 38. #66871 | C22 | semidirect |
| 39. C4⋊(C11⋊C8) | C22 | semidirect |
| 40. C4⋊(C11⋊C8) | C22 | semidirect |
| 44. C2×D4×C11 | Q8 | semidirect |
| 169. C2×D4 | Dic22 | semidirect |
| 199. C11 | #3081 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C11×#518 | 2 |
| #10623050 | 2 |
| #10622828 | 2 |
| C2×#66896 | 2 |
| #10622622 | 2 |
| #10622621 | 2 |
| #10622620 | 2 |
| #10622612 | 2 |
| #10622611 | 2 |
| #10622608 | 2 |
| #3081 | 11 |