Finite Group DatabasebetaFinite Group DatabasebetaOrder 1408.
888 conjugacy classes of subgroups; only the 429 normal subgroups are shown.
This group has 888 conjugacy classes of subgroups — too many to draw. Only its 429 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 |
|---|---|---|
| 5. #10622589 | C2 | direct (N × H) |
| 16. C2×C4×Dic11 | C4 | semidirect |
| 36. C4×Dic11 | C2×C4 | semidirect |
| 47. C2×C4×C11 | C4⋊C4 | semidirect |
| 54. C2×Dic11 | C4⋊C4 | semidirect |
| 74. C4×C11 | C2×C4⋊C4 | semidirect |
| 76. Dic11 | C2×C4⋊C4 | semidirect |
| 89. C2×C11 | #384 | semidirect |
| 114. C11 | C2×#384 | semidirect |
| 131. C2×C4 | Dic11⋊C4 | semidirect |
| 148. C4 | C2×Dic11⋊C4 | semidirect |
| 149. C2 | #10622589 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C11×C4⋊C4 | 2 |
| C22×C4⋊Dic11 | 2 |
| C22×Dic11⋊C4 | 2 |
| C22×C4×Dic11 | 2 |
| #10622589 | 2 |
| C2×#384 | 11 |