Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
786 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 786 conjugacy classes of subgroups — too many to draw. Only its 107 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. #21427740 | C2 | semidirect |
| 4. #21424030 | C2 | semidirect |
| 5. #21422667 | C2 | semidirect |
| 6. #21421944 | C2 | semidirect |
| 128. C22⋊C4×C59 | SD16 | semidirect |
| 262. C59 | #9949 | semidirect |
| 373. C22⋊C4 | #11745670 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21434853 | 2 |
| C2×#16837540 | 2 |
| #21427740 | 2 |
| #21424030 | 2 |
| #21422667 | 2 |
| #21421944 | 2 |
| C59×#1964 | 2 |
| #9949 | 59 |