Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
224 conjugacy classes of subgroups; only the 71 normal subgroups are shown.
This group has 224 conjugacy classes of subgroups — too many to draw. Only its 71 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. #21426369 | C2 | semidirect |
| 4. #21422167 | C2 | semidirect |
| 5. #21422152 | C2 | semidirect |
| 6. #21422151 | C2 | semidirect |
| 66. C59⋊C16 | SD16 | semidirect |
| 127. C59 | #12451 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21426369 | 2 |
| D4×C59⋊C16 | 2 |
| #21423485 | 2 |
| #21422167 | 2 |
| #21422152 | 2 |
| #21422151 | 2 |
| C59×#1673 | 2 |
| #12451 | 59 |