Finite Group DatabasebetaFinite Group DatabasebetaOrder 34432.
552 conjugacy classes of subgroups; only the 197 normal subgroups are shown.
This group has 552 conjugacy classes of subgroups — too many to draw. Only its 197 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 |
|---|---|---|
| 3. #31770984 | C2 | direct (N × H) |
| 46. C2×C4×C269 | Q16 | semidirect |
| 56. C4×C269 | C2×Q16 | semidirect |
| 59. C2×C269 | #494 | semidirect |
| 62. C269 | C2×#494 | semidirect |
| 108. C2×C4 | #16864392 | semidirect |
| 120. C4 | C2×#16864392 | semidirect |
| 122. C2 | #31770984 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#16864392 | 2 |
| C2×#22575453 | 2 |
| #31770984 | 2 |
| C2×C4×#14524130 | 2 |
| C2×C4⋊Q8×C269 | 2 |
| C2×#494 | 269 |