Finite Group DatabasebetaFinite Group DatabasebetaOrder 29824.
252 conjugacy classes of subgroups; only the 61 normal subgroups are shown.
This group has 252 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. #28416489 | C2 | semidirect |
| 3. #28416302 | C2 | semidirect |
| 4. #28416170 | C2 | semidirect |
| 5. #28416169 | C2 | semidirect |
| 6. #28416168 | C2 | semidirect |
| 7. #327×C233 | C2 | semidirect |
| 9. #21418534 | C4 | semidirect |
| 10. #21418531 | C4 | semidirect |
| 14. D4×Dic233 | C4 | semidirect |
| 15. #21418497 | C4 | semidirect |
| 118. C233 | #1514 | semidirect |
| 126. #327 | D233 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #28416980 | 2 |
| #28416489 | 2 |
| #28416302 | 2 |
| #28416170 | 2 |
| #28416169 | 2 |
| #28416168 | 2 |
| #327×C233 | 2 |
| #1514 | 233 |