Finite Group DatabasebetaFinite Group DatabasebetaOrder 1408.
608 conjugacy classes of subgroups; only the 237 normal subgroups are shown.
This group has 608 conjugacy classes of subgroups — too many to draw. Only its 237 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. C2×D4×Dic11 | C2 | semidirect |
| 3. C2×#66896 | C2 | semidirect |
| 4. #10622765 | C2 | direct (N × H) |
| 5. C2×#66881 | C2 | semidirect |
| 6. C2×#66879 | C2 | semidirect |
| 9. C2×C11×D8 | C4 | semidirect |
| 14. D4×Dic11 | C22 | semidirect |
| 18. #66896 | C22 | semidirect |
| 19. #66881 | C22 | semidirect |
| 20. #66879 | C22 | semidirect |
| 24. C2×D4×C11 | C2×C4 | semidirect |
| 31. C11×D8 | C2×C4 | semidirect |
| 32. C2×C8×C11 | C2×C4 | semidirect |
| 49. D4×C11 | C22×C4 | semidirect |
| 59. C8×C11 | C22×C4 | semidirect |
| 81. C2×D8 | Dic11 | semidirect |
| 94. C2×C11 | #442 | semidirect |
| 100. C2×D4 | C2×Dic11 | semidirect |
| 107. D8 | C2×Dic11 | semidirect |
| 110. C2×C8 | C2×Dic11 | semidirect |
| 117. C11 | C2×#442 | semidirect |
| 125. D4 | C22×Dic11 | semidirect |
| 136. C8 | C22×Dic11 | semidirect |
| 150. C2 | #10622765 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C11×D8 | 2 |
| C2×D4×Dic11 | 2 |
| C2×#66896 | 2 |
| #10622765 | 2 |
| C2×#66881 | 2 |
| C2×#66879 | 2 |
| C2×#442 | 11 |