Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
258 conjugacy classes of subgroups; only the 85 normal subgroups are shown.
This group has 258 conjugacy classes of subgroups — too many to draw. Only its 85 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 |
|---|---|---|
| 2. D8×C59⋊C8 | C2 | semidirect |
| 3. #21422890 | C2 | semidirect |
| 4. #21422167 | C2 | semidirect |
| 5. #21422058 | C2 | semidirect |
| 6. C16×C59⋊C8 | C2 | semidirect |
| 7. C59×#1331 | C2 | semidirect |
| 27. #14273668 | C8 | semidirect |
| 49. D8×C59 | C2×C8 | semidirect |
| 64. D472 | C2×C8 | semidirect |
| 68. C59⋊C16 | C2×C8 | semidirect |
| 91. C59⋊C8 | D16 | semidirect |
| 112. #1331 | D59 | semidirect |
| 134. C59 | C8×D16 | semidirect |
| 163. D8 | C8×D59 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×#14273668 | 2 |
| D8×C59⋊C8 | 2 |
| #21422890 | 2 |
| #21422167 | 2 |
| #21422058 | 2 |
| C16×C59⋊C8 | 2 |
| C59×#1331 | 2 |
| C8×D16 | 59 |