Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
564 conjugacy classes of subgroups; only the 95 normal subgroups are shown.
This group has 564 conjugacy classes of subgroups — too many to draw. Only its 95 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. #21435039 | C2 | semidirect |
| 3. #21434441 | C2 | semidirect |
| 4. #21424919 | C2 | semidirect |
| 5. #21422659 | C2 | semidirect |
| 6. #21421940 | C2 | semidirect |
| 7. C59×#1517 | C2 | semidirect |
| 195. #1517 | D59 | semidirect |
| 227. C59 | #10219 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21435039 | 2 |
| #21435011 | 2 |
| #21434441 | 2 |
| #21424919 | 2 |
| #21422659 | 2 |
| #21421940 | 2 |
| C59×#1517 | 2 |
| #10219 | 59 |