Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
372 conjugacy classes of subgroups; only the 59 normal subgroups are shown.
This group has 372 conjugacy classes of subgroups — too many to draw. Only its 59 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 |
|---|---|---|
| 1. #21432368 | C2 | semidirect |
| 3. #21422125 | C2 | semidirect |
| 4. #21422040 | C2 | semidirect |
| 69. C42×C59 | SD16 | semidirect |
| 150. C59 | #12184 | semidirect |
| 207. C42 | #11745670 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21432368 | 2 |
| #21423065 | 2 |
| #21422125 | 2 |
| #21422040 | 2 |
| C59×#2040 | 2 |
| #12184 | 59 |