Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
332 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 332 conjugacy classes of subgroups — too many to draw. Only its 107 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×C4×C59⋊C16 | C2 | semidirect |
| 3. #21422059 | C2 | semidirect |
| 4. #21422056 | C2 | semidirect |
| 5. C59×#1568 | C2 | semidirect |
| 135. #1568 | D59 | semidirect |
| 160. C59 | #11673 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21434666 | 2 |
| C2×C4×C59⋊C16 | 2 |
| #21422059 | 2 |
| #21422056 | 2 |
| C59×#1568 | 2 |
| #11673 | 59 |