Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
466 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 466 conjugacy classes of subgroups — too many to draw. Only its 123 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. #21437199 | C2 | semidirect |
| 3. #21425823 | C2 | semidirect |
| 4. #21422196 | C2 | semidirect |
| 5. C59×#1813 | C2 | semidirect |
| 37. C2×C59⋊C16 | D4 | semidirect |
| 137. #1813 | D59 | semidirect |
| 159. C59 | #13076 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21437199 | 2 |
| #21433758 | 2 |
| #21425823 | 2 |
| #21422196 | 2 |
| C59×#1813 | 2 |
| #13076 | 59 |