Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
552 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 552 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. #21422410 | C2 | semidirect |
| 3. #21422098 | C2 | semidirect |
| 4. C59×#1742 | C2 | semidirect |
| 166. #1742 | D59 | semidirect |
| 191. C59 | #11699 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21429846 | 2 |
| #21422410 | 2 |
| #21422098 | 2 |
| C59×#1742 | 2 |
| #11699 | 59 |