Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
284 conjugacy classes of subgroups; only the 83 normal subgroups are shown.
This group has 284 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. #21426324 | C2 | semidirect |
| 4. #21423694 | C2 | semidirect |
| 6. C16×C59⋊C8 | C2 | semidirect |
| 68. C59⋊C16 | SD16 | semidirect |
| 87. C59⋊C8 | SD32 | semidirect |
| 126. C59 | #12505 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21426376 | 2 |
| #21426351 | 2 |
| #21426324 | 2 |
| #21423694 | 2 |
| #21423685 | 2 |
| C16×C59⋊C8 | 2 |
| C59×#2240 | 2 |
| #12505 | 59 |