Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
494 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 494 conjugacy classes of subgroups — too many to draw. Only its 123 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. #21421921 | C2 | semidirect |
| 175. C59 | #7727 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21432448 | 2 |
| #21424076 | 2 |
| #21421921 | 2 |
| C59×#1817 | 2 |
| #7727 | 59 |