Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
250 conjugacy classes of subgroups; only the 147 normal subgroups are shown.
This group has 250 conjugacy classes of subgroups — too many to draw. Only its 147 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. #21422230 | C2 | semidirect |
| 4. C32×Dic59 | C2 | semidirect |
| 5. C59×#1397 | C2 | semidirect |
| 9. #16837235 | C4 | semidirect |
| 26. C59⋊C32 | C2×C4 | semidirect |
| 30. C32×C59 | C2×C4 | semidirect |
| 68. Dic59 | M64 | semidirect |
| 72. #1397 | D59 | semidirect |
| 87. C59 | C4×M64 | semidirect |
| 102. C32 | C4×D59 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16837235 | 2 |
| C4×C16×D59 | 2 |
| #21422230 | 2 |
| C32×Dic59 | 2 |
| C59×#1397 | 2 |
| C4×M64 | 59 |