Finite Group DatabasebetaFinite Group DatabasebetaOrder 29824.
216 conjugacy classes of subgroups; only the 65 normal subgroups are shown.
This group has 216 conjugacy classes of subgroups — too many to draw. Only its 65 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. #28416486 | C2 | semidirect |
| 3. #28416457 | C2 | semidirect |
| 4. Q8⋊#14272338 | C2 | semidirect |
| 5. #28416164 | C2 | semidirect |
| 6. #28416162 | C2 | semidirect |
| 7. Q8⋊C8×C233 | C2 | semidirect |
| 105. C233 | #1495 | semidirect |
| 111. Q8⋊C8 | D233 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #28416972 | 2 |
| #28416486 | 2 |
| #28416457 | 2 |
| Q8⋊#14272338 | 2 |
| #28416164 | 2 |
| #28416162 | 2 |
| Q8⋊C8×C233 | 2 |
| #1495 | 233 |