Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
510 conjugacy classes of subgroups; only the 135 normal subgroups are shown.
This group has 510 conjugacy classes of subgroups — too many to draw. Only its 135 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. C2×#16837202 | C2 | semidirect |
| 3. C2×C16×Dic59 | C2 | semidirect |
| 4. #21424960 | C2 | semidirect |
| 5. C2×C59×#366 | C2 | semidirect |
| 9. C2×D944 | C4 | semidirect |
| 71. C16×C59 | C22⋊C4 | semidirect |
| 89. C2×Dic59 | D16 | semidirect |
| 117. C2×#366 | D59 | semidirect |
| 140. C59 | #13235 | semidirect |
| 194. C16 | (C2×D59)⋊C4 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×D944 | 2 |
| C2×#16837202 | 2 |
| C2×C16×Dic59 | 2 |
| #21424960 | 2 |
| C2×C59×#366 | 2 |
| #13235 | 59 |