Finite Group DatabasebetaFinite Group DatabasebetaOrder 15296.
262 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 262 conjugacy classes of subgroups — too many to draw. Only its 107 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 |
|---|---|---|
| 1. C2×#16838548 | C2 | semidirect |
| 2. #21439991 | C2 | semidirect |
| 3. #21439990 | C2 | semidirect |
| 4. #21439986 | C2 | semidirect |
| 5. #21439985 | C2 | semidirect |
| 6. #21439980 | C2 | semidirect |
| 7. C2×#16838532 | C2 | semidirect |
| 8. C2×#41×C239 | C2 | semidirect |
| 12. #16838548 | C22 | semidirect |
| 13. C2×Dic478 | C22 | semidirect |
| 14. C2×D956 | C22 | semidirect |
| 17. #16838538 | C22 | semidirect |
| 18. #16838536 | C22 | semidirect |
| 19. #16838535 | C22 | semidirect |
| 20. #16838533 | C22 | semidirect |
| 21. #16838532 | C22 | semidirect |
| 22. #16838532 | C22 | semidirect |
| 23. C2×C239⋊C8 | C22 | semidirect |
| 27. #41×C239 | C22 | semidirect |
| 28. C2×Q8×C239 | C22 | semidirect |
| 30. C2×D4×C239 | C22 | semidirect |
| 81. C239 | #575 | semidirect |
| 84. C2×#41 | D239 | semidirect |
| 98. #41 | C2×D239 | semidirect |
| 100. C2×Q8 | C2×D239 | semidirect |
| 104. C2×D4 | C2×D239 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16838548 | 2 |
| #21439991 | 2 |
| #21439990 | 2 |
| #21439986 | 2 |
| #21439985 | 2 |
| #21439980 | 2 |
| C2×#16838532 | 2 |
| C2×#41×C239 | 2 |
| #575 | 239 |