Finite Group DatabasebetaFinite Group DatabasebetaOrder 1408.
582 conjugacy classes of subgroups; only the 165 normal subgroups are shown.
This group has 582 conjugacy classes of subgroups — too many to draw. Only its 165 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×C42×C11 | C2 | semidirect |
| 4. #10622824 | C2 | semidirect |
| 5. #10622823 | C2 | semidirect |
| 6. #10622553 | C2 | semidirect |
| 7. #10622546 | C2 | semidirect |
| 67. C22×C42 | D11 | semidirect |
| 127. C11 | #2853 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C42×C11 | 2 |
| C2×#66982 | 2 |
| #10622826 | 2 |
| #10622824 | 2 |
| #10622823 | 2 |
| #10622553 | 2 |
| #10622546 | 2 |
| #2853 | 11 |