Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
240 conjugacy classes of subgroups; only the 67 normal subgroups are shown.
This group has 240 conjugacy classes of subgroups — too many to draw. Only its 67 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 |
|---|---|---|
| 3. Q16×C59⋊C8 | C2 | semidirect |
| 4. #21422165 | C2 | semidirect |
| 5. #21422145 | C2 | semidirect |
| 7. C59×#2209 | C2 | semidirect |
| 109. #2209 | D59 | semidirect |
| 135. C59 | #12429 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21426136 | 2 |
| #21423703 | 2 |
| Q16×C59⋊C8 | 2 |
| #21422165 | 2 |
| #21422145 | 2 |
| #21422143 | 2 |
| C59×#2209 | 2 |
| #12429 | 59 |