Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
636 conjugacy classes of subgroups; only the 391 normal subgroups are shown.
This group has 636 conjugacy classes of subgroups — too many to draw. Only its 391 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. #21425869 | C2 | semidirect |
| 4. C2×#16837225 | C2 | semidirect |
| 16. C59×#504 | C4 | semidirect |
| 35. M32×C59 | C2×C4 | semidirect |
| 37. C2×C16×C59 | C2×C4 | semidirect |
| 92. #504 | Dic59 | semidirect |
| 101. C59 | #33404 | semidirect |
| 113. M32 | C2×Dic59 | semidirect |
| 115. C2×C16 | C2×Dic59 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21432707 | 2 |
| #21432691 | 2 |
| #21425869 | 2 |
| C2×#16837225 | 2 |
| C59×#3407 | 2 |
| #33404 | 59 |