Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
500 conjugacy classes of subgroups; only the 81 normal subgroups are shown.
This group has 500 conjugacy classes of subgroups — too many to draw. Only its 81 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 |
|---|---|---|
| 2. #21434127 | C2 | semidirect |
| 3. #21422730 | C2 | semidirect |
| 4. #21422565 | C2 | semidirect |
| 5. #21422440 | C2 | semidirect |
| 6. #21421957 | C2 | semidirect |
| 7. C59×#3112 | C2 | semidirect |
| 192. #3112 | D59 | semidirect |
| 229. C59 | #10040 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21435091 | 2 |
| #21434127 | 2 |
| #21422730 | 2 |
| #21422565 | 2 |
| #21422440 | 2 |
| #21421957 | 2 |
| C59×#3112 | 2 |
| #10040 | 59 |