Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
398 conjugacy classes of subgroups; only the 55 normal subgroups are shown.
This group has 398 conjugacy classes of subgroups — too many to draw. Only its 55 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 |
|---|---|---|
| 1. #21431925 | C2 | semidirect |
| 2. #21423133 | C2 | semidirect |
| 4. #21422122 | C2 | semidirect |
| 5. #21422098 | C2 | semidirect |
| 6. #21422042 | C2 | semidirect |
| 7. C59×#2039 | C2 | semidirect |
| 185. #2039 | D59 | semidirect |
| 217. C59 | #12144 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21431925 | 2 |
| #21423133 | 2 |
| #21423031 | 2 |
| #21422122 | 2 |
| #21422098 | 2 |
| #21422042 | 2 |
| C59×#2039 | 2 |
| #12144 | 59 |