Finite Group DatabasebetaFinite Group DatabasebetaOrder 29824.
202 conjugacy classes of subgroups; only the 65 normal subgroups are shown.
This group has 202 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 |
|---|---|---|
| 4. #28416167 | C2 | semidirect |
| 5. Q8⋊#14272338 | C2 | semidirect |
| 6. #28416165 | C2 | semidirect |
| 7. Q8⋊C8×C233 | C2 | semidirect |
| 99. C233 | #1497 | semidirect |
| 107. Q8⋊C8 | D233 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #28416989 | 2 |
| #28416491 | 2 |
| #28416486 | 2 |
| #28416167 | 2 |
| Q8⋊#14272338 | 2 |
| #28416165 | 2 |
| Q8⋊C8×C233 | 2 |
| #1497 | 233 |