Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
248 conjugacy classes of subgroups; only the 71 normal subgroups are shown.
This group has 248 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 |
|---|---|---|
| 2. Q8×C59⋊C16 | C2 | semidirect |
| 3. #21423456 | C2 | semidirect |
| 4. #21422167 | C2 | semidirect |
| 5. #21422142 | C2 | semidirect |
| 6. #21422141 | C2 | semidirect |
| 7. C59×#1668 | C2 | semidirect |
| 71. C59⋊C16 | SD16 | semidirect |
| 75. Q8×C59 | D16 | semidirect |
| 115. #1668 | D59 | semidirect |
| 139. C59 | #12439 | semidirect |
| 192. Q8 | #14273668 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21426345 | 2 |
| Q8×C59⋊C16 | 2 |
| #21423456 | 2 |
| #21422167 | 2 |
| #21422142 | 2 |
| #21422141 | 2 |
| C59×#1668 | 2 |
| #12439 | 59 |