Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
508 conjugacy classes of subgroups; only the 101 normal subgroups are shown.
This group has 508 conjugacy classes of subgroups — too many to draw. Only its 101 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 |
|---|---|---|
| 4. #21421975 | C2 | semidirect |
| 5. #21421963 | C2 | semidirect |
| 6. #21421944 | C2 | semidirect |
| 7. C59×#2549 | C2 | semidirect |
| 27. C22×D236 | Q8 | semidirect |
| 36. C2×C4⋊Dic59 | Q8 | semidirect |
| 220. #2549 | D59 | semidirect |
| 256. C59 | #10374 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21424932 | 2 |
| #21422663 | 2 |
| C2×#16837135 | 2 |
| #21421975 | 2 |
| #21421963 | 2 |
| #21421944 | 2 |
| C59×#2549 | 2 |
| #10374 | 59 |