Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
234 conjugacy classes of subgroups; only the 65 normal subgroups are shown.
This group has 234 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 |
|---|---|---|
| 3. #21423713 | C2 | semidirect |
| 5. #21422165 | C2 | semidirect |
| 6. #21422152 | C2 | semidirect |
| 7. C59×#1364 | C2 | semidirect |
| 64. D472 | Q16 | semidirect |
| 109. #1364 | D59 | semidirect |
| 129. C59 | #12445 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21426234 | 2 |
| #21426230 | 2 |
| #21423713 | 2 |
| #21422890 | 2 |
| #21422165 | 2 |
| #21422152 | 2 |
| C59×#1364 | 2 |
| #12445 | 59 |