Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
530 conjugacy classes of subgroups; only the 103 normal subgroups are shown.
This group has 530 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×#16837697 | C2 | semidirect |
| 4. #21422780 | C2 | semidirect |
| 6. #21421992 | C2 | semidirect |
| 7. C59×#1461 | C2 | semidirect |
| 82. C2×Q8×C59 | SD16 | semidirect |
| 199. #1461 | D59 | semidirect |
| 230. C59 | #10181 | semidirect |
| 290. C2×Q8 | #11745660 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21435023 | 2 |
| C2×#16837697 | 2 |
| #21433568 | 2 |
| #21422780 | 2 |
| #21422496 | 2 |
| #21421992 | 2 |
| C59×#1461 | 2 |
| #10181 | 59 |