Finite Group DatabasebetaFinite Group DatabasebetaOrder 34432.
176 conjugacy classes of subgroups; only the 61 normal subgroups are shown.
This group has 176 conjugacy classes of subgroups — too many to draw. Only its 61 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. #31770683 | C2 | semidirect |
| 3. #31770682 | C2 | semidirect |
| 4. #31770355 | C2 | semidirect |
| 5. #31770334 | C2 | semidirect |
| 6. #31770327 | C2 | semidirect |
| 7. D4⋊C8×C269 | C2 | semidirect |
| 52. #14524130 | M16 | semidirect |
| 83. C269 | #1594 | semidirect |
| 90. D4⋊C8 | D269 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×#16864387 | 2 |
| #31770683 | 2 |
| #31770682 | 2 |
| #31770355 | 2 |
| #31770334 | 2 |
| #31770327 | 2 |
| D4⋊C8×C269 | 2 |
| #1594 | 269 |