Finite Group DatabasebetaFinite Group DatabasebetaOrder 30592.
284 conjugacy classes of subgroups; only the 109 normal subgroups are shown.
This group has 284 conjugacy classes of subgroups — too many to draw. Only its 109 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. #29504727 | C2 | semidirect |
| 5. #29504544 | C2 | semidirect |
| 6. #29504542 | C2 | semidirect |
| 7. #405×C239 | C2 | semidirect |
| 15. C2×#16838531 | C4 | semidirect |
| 16. C2×C8×D239 | C4 | semidirect |
| 18. #21439878 | C4 | semidirect |
| 19. #21439876 | C4 | semidirect |
| 106. C239 | #1757 | semidirect |
| 112. #405 | D239 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#21439966 | 2 |
| #29504754 | 2 |
| #29504745 | 2 |
| #29504727 | 2 |
| #29504544 | 2 |
| #29504542 | 2 |
| #405×C239 | 2 |
| #1757 | 239 |