Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
250 conjugacy classes of subgroups; only the 151 normal subgroups are shown.
This group has 250 conjugacy classes of subgroups — too many to draw. Only its 151 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. #21422229 | C2 | semidirect |
| 4. C4×C59⋊C32 | C2 | semidirect |
| 5. C4×C32×C59 | C2 | semidirect |
| 9. #16837235 | C4 | direct (N × H) |
| 26. C59⋊C32 | C2×C4 | semidirect |
| 30. C32×C59 | C2×C4 | semidirect |
| 64. C4×C59 | M64 | semidirect |
| 73. C4×C32 | D59 | semidirect |
| 87. C59 | C4×M64 | semidirect |
| 102. C32 | C4×D59 | semidirect |
| 137. C4 | #16837235 | direct (N × H) |
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 |
| #21422229 | 2 |
| C4×C59⋊C32 | 2 |
| C4×C32×C59 | 2 |
| C4×M64 | 59 |