Finite Group DatabasebetaFinite Group DatabasebetaOrder 15296.
266 conjugacy classes of subgroups; only the 103 normal subgroups are shown.
This group has 266 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 |
|---|---|---|
| 1. C2×#16838549 | C2 | semidirect |
| 2. C2×#16838547 | C2 | semidirect |
| 3. #21439981 | C2 | direct (N × H) |
| 4. C2×#16838538 | C2 | semidirect |
| 5. C2×#16838537 | C2 | semidirect |
| 6. C2×#16838533 | C2 | semidirect |
| 7. C2×C8×D239 | C2 | semidirect |
| 8. C2×SD16×C239 | C2 | semidirect |
| 10. #16838549 | C22 | semidirect |
| 12. #16838547 | C22 | semidirect |
| 20. #16838538 | C22 | semidirect |
| 21. #16838537 | C22 | semidirect |
| 22. #16838533 | C22 | semidirect |
| 24. C8×D239 | C22 | semidirect |
| 27. SD16×C239 | C22 | semidirect |
| 65. C2×C239 | #135 | semidirect |
| 69. C239 | C2×#135 | semidirect |
| 76. C2×SD16 | D239 | semidirect |
| 94. SD16 | C2×D239 | semidirect |
| 137. C2 | #21439981 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16838549 | 2 |
| C2×#16838547 | 2 |
| #21439981 | 2 |
| C2×#16838538 | 2 |
| C2×#16838537 | 2 |
| C2×#16838533 | 2 |
| C2×C8×D239 | 2 |
| C2×SD16×C239 | 2 |
| C2×#135 | 239 |