Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
430 conjugacy classes of subgroups; only the 93 normal subgroups are shown.
This group has 430 conjugacy classes of subgroups — too many to draw. Only its 93 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. #21425043 | C2 | semidirect |
| 4. #21422814 | C2 | semidirect |
| 6. #21421951 | C2 | semidirect |
| 7. C59×#1290 | C2 | semidirect |
| 10. #16837796 | C4 | semidirect |
| 11. #16837771 | C4 | semidirect |
| 189. #1290 | D59 | semidirect |
| 222. C59 | #9376 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21435125 | 2 |
| #21433232 | 2 |
| #21425043 | 2 |
| #21422814 | 2 |
| #21422622 | 2 |
| #21421951 | 2 |
| C59×#1290 | 2 |
| #9376 | 59 |