Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
212 conjugacy classes of subgroups; only the 65 normal subgroups are shown.
This group has 212 conjugacy classes of subgroups — too many to draw. Only its 65 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. #21425942 | C2 | semidirect |
| 3. #21422273 | C2 | semidirect |
| 4. #21422229 | C2 | semidirect |
| 5. C59×#1424 | C2 | semidirect |
| 8. D1888 | C4 | semidirect |
| 17. D944 | C2×C4 | semidirect |
| 24. C32×C59 | C2×C4 | semidirect |
| 58. #1424 | D59 | semidirect |
| 72. C59 | #13654 | semidirect |
| 83. C32 | C4×D59 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×D1888 | 2 |
| #21425942 | 2 |
| #21422273 | 2 |
| #21422229 | 2 |
| C59×#1424 | 2 |
| #13654 | 59 |