Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
288 conjugacy classes of subgroups; only the 63 normal subgroups are shown.
This group has 288 conjugacy classes of subgroups — too many to draw. Only its 63 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. C2×#16837242 | C2 | semidirect |
| 3. C2×#16837239 | C2 | semidirect |
| 4. #21422276 | C2 | semidirect |
| 5. #21422273 | C2 | semidirect |
| 6. C22⋊(C59⋊C32) | C2 | semidirect |
| 7. C59×#2216 | C2 | semidirect |
| 109. #2216 | D59 | semidirect |
| 133. C59 | #13666 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16837834 | 2 |
| C2×#16837242 | 2 |
| C2×#16837239 | 2 |
| #21422276 | 2 |
| #21422273 | 2 |
| C22⋊(C59⋊C32) | 2 |
| C59×#2216 | 2 |
| #13666 | 59 |