Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
594 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 594 conjugacy classes of subgroups — too many to draw. Only its 99 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 |
|---|---|---|
| 3. #21428581 | C2 | semidirect |
| 4. #21424180 | C2 | semidirect |
| 5. #21422667 | C2 | semidirect |
| 6. #21421944 | C2 | semidirect |
| 242. C59 | #9953 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21434853 | 2 |
| C2×#16837713 | 2 |
| #21428581 | 2 |
| #21424180 | 2 |
| #21422667 | 2 |
| #21421944 | 2 |
| C59×#1964 | 2 |
| #9953 | 59 |