Finite Group DatabasebetaFinite Group DatabasebetaOrder 29824.
158 conjugacy classes of subgroups; only the 67 normal subgroups are shown.
This group has 158 conjugacy classes of subgroups — too many to draw. Only its 67 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. #28416187 | C2 | semidirect |
| 5. #28416186 | C2 | semidirect |
| 6. #28416185 | C2 | semidirect |
| 7. #335×C233 | C2 | semidirect |
| 75. C233 | #1574 | semidirect |
| 81. #335 | D233 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #28416487 | 2 |
| #28416486 | 2 |
| #28416457 | 2 |
| #28416187 | 2 |
| #28416186 | 2 |
| #28416185 | 2 |
| #335×C233 | 2 |
| #1574 | 233 |