Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
302 conjugacy classes of subgroups; only the 83 normal subgroups are shown.
This group has 302 conjugacy classes of subgroups — too many to draw. Only its 83 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 |
|---|---|---|
| 1. #21426376 | C2 | semidirect |
| 3. #21426321 | C2 | semidirect |
| 4. #21426319 | C2 | semidirect |
| 5. #21423688 | C2 | semidirect |
| 6. #21422013 | C2 | semidirect |
| 7. C59×#1706 | C2 | semidirect |
| 69. C59⋊C16 | SD16 | semidirect |
| 110. #1706 | D59 | semidirect |
| 132. C59 | #12506 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21426376 | 2 |
| #21426345 | 2 |
| #21426321 | 2 |
| #21426319 | 2 |
| #21423688 | 2 |
| #21422013 | 2 |
| C59×#1706 | 2 |
| #12506 | 59 |