Finite Group DatabasebetaFinite Group DatabasebetaOrder 15296.
258 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 258 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. #21440007 | C2 | semidirect |
| 2. #21440006 | C2 | semidirect |
| 3. #21439993 | C2 | semidirect |
| 4. #21439988 | C2 | semidirect |
| 5. #21439982 | C2 | semidirect |
| 6. C2×#16838537 | C2 | semidirect |
| 7. #131×C239 | C2 | semidirect |
| 10. #16838548 | C22 | semidirect |
| 12. C2×Dic478 | C22 | semidirect |
| 16. Dic956 | C22 | semidirect |
| 17. #16838537 | C22 | semidirect |
| 18. #16838537 | C22 | semidirect |
| 19. #16838537 | C22 | semidirect |
| 20. D1912 | C22 | semidirect |
| 22. M16×C239 | C22 | semidirect |
| 23. C2×C8×C239 | C22 | semidirect |
| 53. C239 | #577 | semidirect |
| 61. #131 | D239 | semidirect |
| 76. M16 | C2×D239 | semidirect |
| 77. C2×C8 | C2×D239 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21440007 | 2 |
| #21440006 | 2 |
| #21439993 | 2 |
| #21439988 | 2 |
| #21439982 | 2 |
| C2×#16838537 | 2 |
| #131×C239 | 2 |
| #577 | 239 |