Finite Group DatabasebetaFinite Group DatabasebetaOrder 15296.
114 conjugacy classes of subgroups; only the 41 normal subgroups are shown.
This group has 114 conjugacy classes of subgroups — too many to draw. Only its 41 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×#16838538 | C2 | semidirect |
| 5. #21439893 | C2 | semidirect |
| 6. #21439885 | C2 | semidirect |
| 7. #103×C239 | C2 | semidirect |
| 39. C2×D239 | Q16 | semidirect |
| 51. C239 | #467 | semidirect |
| 59. #103 | D239 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16838538 | 2 |
| C2×C8×D239 | 2 |
| #21439940 | 2 |
| #21439936 | 2 |
| #21439893 | 2 |
| #21439885 | 2 |
| #103×C239 | 2 |
| #467 | 239 |