Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
416 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 416 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 |
|---|---|---|
| 2. #21424125 | C2 | semidirect |
| 3. #21422109 | C2 | semidirect |
| 4. #21422106 | C2 | semidirect |
| 5. C59×#2112 | C2 | semidirect |
| 6. C2×#14273749 | C4 | semidirect |
| 8. #16837643 | C4 | semidirect |
| 10. #16837638 | C4 | semidirect |
| 14. #16837440 | C4 | semidirect |
| 170. #2112 | D59 | semidirect |
| 199. C59 | #11890 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21433677 | 2 |
| #21424125 | 2 |
| #21422109 | 2 |
| #21422106 | 2 |
| C59×#2112 | 2 |
| #11890 | 59 |