Finite Group DatabasebetaFinite Group DatabasebetaOrder 15296.
258 conjugacy classes of subgroups; only the 111 normal subgroups are shown.
This group has 258 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 |
|---|---|---|
| 2. #21439991 | C2 | direct (N × H) |
| 3. C2×#16838538 | C2 | semidirect |
| 4. C2×#16838535 | C2 | semidirect |
| 5. C2×#16838532 | C2 | semidirect |
| 6. C22×Q8×C239 | C2 | semidirect |
| 13. #16838538 | C22 | semidirect |
| 14. #16838535 | C22 | semidirect |
| 15. #16838532 | C22 | semidirect |
| 20. C2×Q8×C239 | C22 | semidirect |
| 53. C2×C239 | #137 | semidirect |
| 56. C239 | C2×#137 | semidirect |
| 59. C22×Q8 | D239 | semidirect |
| 70. C2×Q8 | C2×D239 | semidirect |
| 111. C2 | #21439991 | 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 |
| #21439991 | 2 |
| C2×#16838538 | 2 |
| C2×#16838535 | 2 |
| C2×#16838532 | 2 |
| C22×Q8×C239 | 2 |
| C2×#137 | 239 |