Finite Group DatabasebetaFinite Group DatabasebetaOrder 15296.
266 conjugacy classes of subgroups; only the 111 normal subgroups are shown.
This group has 266 conjugacy classes of subgroups — too many to draw. Only its 111 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. #21439980 | C2 | direct (N × H) |
| 3. C2×#16838538 | C2 | semidirect |
| 4. C2×#16838536 | C2 | semidirect |
| 5. C2×#16838535 | C2 | semidirect |
| 6. C2×#16838533 | C2 | semidirect |
| 7. C22×C239⋊C8 | C2 | semidirect |
| 8. C2×#41×C239 | C2 | semidirect |
| 10. #16838548 | C22 | semidirect |
| 15. #16838538 | C22 | semidirect |
| 16. #16838536 | C22 | semidirect |
| 17. #16838535 | C22 | semidirect |
| 18. #16838533 | C22 | semidirect |
| 21. C2×C239⋊C8 | C22 | semidirect |
| 23. #41×C239 | C22 | semidirect |
| 66. C2×C239 | #135 | semidirect |
| 69. C239 | C2×#135 | semidirect |
| 72. C2×#41 | D239 | semidirect |
| 82. #41 | C2×D239 | semidirect |
| 137. C2 | #21439980 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16838548 | 2 |
| #21439980 | 2 |
| C2×#16838538 | 2 |
| C2×#16838536 | 2 |
| C2×#16838535 | 2 |
| C2×#16838533 | 2 |
| C22×C239⋊C8 | 2 |
| C2×#41×C239 | 2 |
| C2×#135 | 239 |