Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
270 conjugacy classes of subgroups; only the 67 normal subgroups are shown.
This group has 270 conjugacy classes of subgroups — too many to draw. Only its 67 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. #21422180 | C2 | semidirect |
| 3. C59×#1275 | C2 | semidirect |
| 15. C2×D472 | C8 | semidirect |
| 113. #1275 | D59 | semidirect |
| 127. C59 | #7110 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21424972 | 2 |
| #21422180 | 2 |
| C59×#1275 | 2 |
| #7110 | 59 |