Finite Group DatabasebetaFinite Group DatabasebetaOrder 1408.
1072 conjugacy classes of subgroups; only the 469 normal subgroups are shown.
This group has 1072 conjugacy classes of subgroups — too many to draw. Only its 469 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. C23×C11⋊C8 | C2 | semidirect |
| 3. C2×C22⋊(C11⋊C8) | C2 | direct (N × H) |
| 11. C22×C11⋊C8 | C22 | semidirect |
| 12. C22⋊(C11⋊C8) | C22 | direct (N × H) |
| 15. C24×C11 | C8 | semidirect |
| 28. C2×C11⋊C8 | C23 | semidirect |
| 35. C23×C11 | C2×C8 | semidirect |
| 54. C22×C11 | C22⋊C8 | semidirect |
| 57. C22×C11 | C22×C8 | semidirect |
| 73. C2×C11 | C2×C22⋊C8 | semidirect |
| 79. C24 | C11⋊C8 | semidirect |
| 93. C11 | C22×C22⋊C8 | semidirect |
| 98. C23 | C2×C11⋊C8 | semidirect |
| 115. C22 | C22⋊(C11⋊C8) | direct (N × H) |
| 117. C22 | C22×C11⋊C8 | semidirect |
| 125. C2 | C2×C22⋊(C11⋊C8) | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C24×C4×C11 | 2 |
| C23×C11⋊C8 | 2 |
| C2×C22⋊(C11⋊C8) | 2 |
| C22×C22⋊C8 | 11 |