Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
260 conjugacy classes of subgroups; only the 75 normal subgroups are shown.
This group has 260 conjugacy classes of subgroups — too many to draw. Only its 75 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. #21426323 | C2 | semidirect |
| 4. #21423705 | C2 | semidirect |
| 6. C16×C59⋊C8 | C2 | semidirect |
| 7. C59×#2241 | C2 | semidirect |
| 99. #2241 | D59 | semidirect |
| 124. C59 | #12511 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21426323 | 2 |
| #21426321 | 2 |
| #21426320 | 2 |
| #21423705 | 2 |
| #21423703 | 2 |
| C16×C59⋊C8 | 2 |
| C59×#2241 | 2 |
| #12511 | 59 |