Finite Group DatabasebetaFinite Group DatabasebetaOrder 29824.
284 conjugacy classes of subgroups; only the 63 normal subgroups are shown.
This group has 284 conjugacy classes of subgroups — too many to draw. Only its 63 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. C22⋊C8×D233 | C2 | semidirect |
| 3. #28416297 | C2 | semidirect |
| 4. #28416172 | C2 | semidirect |
| 5. #28416170 | C2 | semidirect |
| 6. #28416168 | C2 | semidirect |
| 7. #328×C233 | C2 | semidirect |
| 8. C2×#16836595 | C4 | semidirect |
| 12. #21418511 | C4 | semidirect |
| 13. #21418510 | C4 | semidirect |
| 18. #21418493 | C4 | semidirect |
| 127. C233 | #1516 | semidirect |
| 133. #328 | D233 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #28416948 | 2 |
| C22⋊C8×D233 | 2 |
| #28416297 | 2 |
| #28416172 | 2 |
| #28416170 | 2 |
| #28416168 | 2 |
| #328×C233 | 2 |
| #1516 | 233 |