Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
460 conjugacy classes of subgroups; only the 97 normal subgroups are shown.
This group has 460 conjugacy classes of subgroups — too many to draw. Only its 97 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. #21424085 | C2 | semidirect |
| 3. #21422774 | C2 | semidirect |
| 4. #21422548 | C2 | semidirect |
| 5. C2×#16837131 | C2 | semidirect |
| 6. #21421970 | C2 | semidirect |
| 7. C59×#1567 | C2 | semidirect |
| 196. #1567 | D59 | semidirect |
| 229. C59 | #10456 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21433562 | 2 |
| #21424085 | 2 |
| #21422774 | 2 |
| #21422548 | 2 |
| C2×#16837131 | 2 |
| #21421970 | 2 |
| C59×#1567 | 2 |
| #10456 | 59 |