Finite Group DatabasebetaFinite Group DatabasebetaOrder 15296.
258 conjugacy classes of subgroups; only the 103 normal subgroups are shown.
This group has 258 conjugacy classes of subgroups — too many to draw. Only its 103 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. C2×Q8×D239 | C2 | semidirect |
| 3. #21439989 | C2 | direct (N × H) |
| 4. C2×Dic956 | C2 | semidirect |
| 5. C2×#16838538 | C2 | semidirect |
| 6. C2×#16838536 | C2 | semidirect |
| 7. C2×#16838531 | C2 | semidirect |
| 8. C2×SD16×C239 | C2 | semidirect |
| 15. Q8×D239 | C22 | semidirect |
| 20. Dic956 | C22 | semidirect |
| 21. #16838538 | C22 | semidirect |
| 22. #16838536 | C22 | semidirect |
| 23. #16838531 | C22 | semidirect |
| 27. SD16×C239 | C22 | semidirect |
| 64. C2×C239 | #137 | semidirect |
| 67. C239 | C2×#137 | semidirect |
| 75. C2×SD16 | D239 | semidirect |
| 93. SD16 | C2×D239 | semidirect |
| 133. C2 | #21439989 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16838547 | 2 |
| C2×Q8×D239 | 2 |
| #21439989 | 2 |
| C2×Dic956 | 2 |
| C2×#16838538 | 2 |
| C2×#16838536 | 2 |
| C2×#16838531 | 2 |
| C2×SD16×C239 | 2 |
| C2×#137 | 239 |