Finite Group DatabasebetaFinite Group DatabasebetaOrder 29824.
256 conjugacy classes of subgroups; only the 61 normal subgroups are shown.
This group has 256 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. #28416490 | C2 | semidirect |
| 3. #97×D233 | C2 | semidirect |
| 4. #28416175 | C2 | semidirect |
| 5. #28416174 | C2 | semidirect |
| 6. #28416174 | C2 | semidirect |
| 7. #329×C233 | C2 | semidirect |
| 109. C233 | #1530 | semidirect |
| 117. #329 | D233 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #28416984 | 2 |
| #28416490 | 2 |
| #97×D233 | 2 |
| #28416175 | 2 |
| #28416174 | 2 |
| #329×C233 | 2 |
| #1530 | 233 |