Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
226 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 226 conjugacy classes of subgroups — too many to draw. Only its 89 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 |
|---|---|---|
| 4. #21422162 | C2 | semidirect |
| 5. #21422161 | C2 | semidirect |
| 6. #21422161 | C2 | semidirect |
| 7. C59×#1368 | C2 | semidirect |
| 64. C16×C59 | M16 | semidirect |
| 66. C59⋊C16 | M16 | semidirect |
| 105. #1368 | D59 | semidirect |
| 125. C59 | #12019 | semidirect |
| 169. C16 | #11745659 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #346×D59 | 2 |
| #21422856 | 2 |
| #21422850 | 2 |
| #21422162 | 2 |
| #21422161 | 2 |
| C59×#1368 | 2 |
| #12019 | 59 |