Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
530 conjugacy classes of subgroups; only the 105 normal subgroups are shown.
This group has 530 conjugacy classes of subgroups — too many to draw. Only its 105 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×#16837697 | C2 | semidirect |
| 3. #21422782 | C2 | semidirect |
| 5. #21422420 | C2 | semidirect |
| 6. #21421991 | C2 | semidirect |
| 87. C2×Q8×C59 | SD16 | semidirect |
| 230. C59 | #10181 | semidirect |
| 290. C2×Q8 | #11745670 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21435018 | 2 |
| C2×#16837697 | 2 |
| #21422782 | 2 |
| #21422495 | 2 |
| #21422420 | 2 |
| #21421991 | 2 |
| C59×#3037 | 2 |
| #10181 | 59 |