Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
650 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 650 conjugacy classes of subgroups — too many to draw. Only its 99 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. #21435016 | C2 | semidirect |
| 2. #21435011 | C2 | semidirect |
| 3. #21434541 | C2 | semidirect |
| 4. #21424919 | C2 | semidirect |
| 5. #21422655 | C2 | semidirect |
| 6. #21421940 | C2 | semidirect |
| 7. C59×#1517 | C2 | semidirect |
| 131. C2×C59⋊C8 | D8 | semidirect |
| 210. #1517 | D59 | semidirect |
| 243. C59 | #10218 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21435016 | 2 |
| #21435011 | 2 |
| #21434541 | 2 |
| #21424919 | 2 |
| #21422655 | 2 |
| #21421940 | 2 |
| C59×#1517 | 2 |
| #10218 | 59 |