Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
296 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 296 conjugacy classes of subgroups — too many to draw. Only its 89 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. #21424271 | C2 | semidirect |
| 4. #21422208 | C2 | semidirect |
| 5. C59×#1375 | C2 | semidirect |
| 109. #1375 | D59 | semidirect |
| 126. C59 | #13486 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21425846 | 2 |
| #21424989 | 2 |
| #21424271 | 2 |
| #21422208 | 2 |
| C59×#1375 | 2 |
| #13486 | 59 |