Finite Group DatabasebetaFinite Group DatabasebetaOrder 29824.
326 conjugacy classes of subgroups; only the 73 normal subgroups are shown.
This group has 326 conjugacy classes of subgroups — too many to draw. Only its 73 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. #28416298 | C2 | semidirect |
| 3. #28416170 | C2 | semidirect |
| 4. #407×C233 | C2 | semidirect |
| 5. C22×D932 | C4 | semidirect |
| 9. #21418509 | C4 | semidirect |
| 11. C2×C4⋊Dic233 | C4 | semidirect |
| 15. #21418442 | C22 | semidirect |
| 19. C22⋊C8×C233 | C22 | semidirect |
| 102. C233 | #1510 | semidirect |
| 105. #407 | D233 | semidirect |
| 120. C22⋊C8 | C2×D233 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#21418509 | 2 |
| #28416298 | 2 |
| #28416170 | 2 |
| #407×C233 | 2 |
| #1510 | 233 |