Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
298 conjugacy classes of subgroups; only the 67 normal subgroups are shown.
This group has 298 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 |
|---|---|---|
| 1. C2×#16837239 | C2 | semidirect |
| 2. C2×#16837237 | C2 | semidirect |
| 3. #21426182 | C2 | semidirect |
| 4. #21422277 | C2 | semidirect |
| 5. #21422274 | C2 | semidirect |
| 6. C22⋊(C59⋊C32) | C2 | semidirect |
| 7. C2×C59×#508 | C2 | semidirect |
| 39. Q32×C59 | D4 | semidirect |
| 42. D16×C59 | D4 | semidirect |
| 109. C2×#508 | D59 | semidirect |
| 137. C59 | #13663 | semidirect |
| 148. Q32 | C22⋊D59 | semidirect |
| 153. D16 | C22⋊D59 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16837239 | 2 |
| C2×#16837237 | 2 |
| #21426182 | 2 |
| #21422277 | 2 |
| #21422274 | 2 |
| C22⋊(C59⋊C32) | 2 |
| C2×C59×#508 | 2 |
| #13663 | 59 |