Finite Group DatabasebetaFinite Group DatabasebetaOrder 30592.
688 conjugacy classes of subgroups; only the 173 normal subgroups are shown.
This group has 688 conjugacy classes of subgroups — too many to draw. Only its 173 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. #29504675 | C2 | semidirect |
| 3. #29504672 | C2 | semidirect |
| 4. #29504666 | C2 | semidirect |
| 5. #29504664 | C2 | semidirect |
| 6. #29504661 | C2 | semidirect |
| 7. #29504651 | C2 | semidirect |
| 8. #29504627 | C2 | semidirect |
| 9. #386×C239 | C2 | semidirect |
| 12. #21439928 | C4 | semidirect |
| 13. C2×C4⋊Dic239 | C22 | semidirect |
| 14. C2×Dic239⋊C4 | C22 | semidirect |
| 17. C2×C22⋊Dic239 | C22 | semidirect |
| 23. C2×C4×Dic239 | C22 | semidirect |
| 24. C2×C4×Dic239 | C22 | semidirect |
| 25. C239⋊#95 | C22 | semidirect |
| 26. C239⋊#95 | C22 | semidirect |
| 28. C23×C4×C239 | C22 | semidirect |
| 30. C2×C22⋊C4×C239 | C22 | semidirect |
| 31. #95×C239 | C22 | semidirect |
| 36. C23×D239 | C2×C4 | semidirect |
| 48. C22⋊Dic239 | C2×C4 | semidirect |
| 53. (C2×D239)⋊C4 | C2×C4 | semidirect |
| 149. C239 | #2375 | semidirect |
| 158. #386 | D239 | semidirect |
| 163. C23×C4 | C2×D239 | semidirect |
| 176. C2×C22⋊C4 | C2×D239 | semidirect |
| 181. #95 | C2×D239 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#21439928 | 2 |
| #29504675 | 2 |
| #29504672 | 2 |
| #29504666 | 2 |
| #29504664 | 2 |
| #29504661 | 2 |
| #29504651 | 2 |
| #29504627 | 2 |
| #386×C239 | 2 |
| #2375 | 239 |