Finite Group DatabasebetaFinite Group DatabasebetaOrder 34432.
226 conjugacy classes of subgroups; only the 57 normal subgroups are shown.
This group has 226 conjugacy classes of subgroups — too many to draw. Only its 57 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×Dic1076 | C2 | semidirect |
| 2. C2×#22575398 | C2 | semidirect |
| 4. #31770410 | C2 | semidirect |
| 5. C22⋊C16×C269 | C2 | semidirect |
| 26. Dic1076 | D4 | semidirect |
| 54. C22×C269 | SD32 | semidirect |
| 69. C269 | #2185 | semidirect |
| 75. C22⋊C16 | D269 | semidirect |
| 127. C22 | #22575398 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×Dic1076 | 2 |
| C2×#22575398 | 2 |
| #31770841 | 2 |
| #31770410 | 2 |
| C22⋊C16×C269 | 2 |
| #2185 | 269 |