Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
418 conjugacy classes of subgroups; only the 73 normal subgroups are shown.
This group has 418 conjugacy classes of subgroups — too many to draw. Only its 73 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. #21426321 | C2 | semidirect |
| 3. #21426240 | C2 | semidirect |
| 4. #21422141 | C2 | semidirect |
| 5. #21422056 | C2 | semidirect |
| 6. D4⋊(C59⋊C16) | C2 | semidirect |
| 7. C59×#1675 | C2 | semidirect |
| 16. C4⋊(C59⋊C16) | C22 | semidirect |
| 19. C4×C59⋊C16 | C22 | semidirect |
| 20. C59×#500 | C22 | semidirect |
| 23. C59×#335 | C22 | semidirect |
| 147. #1675 | D59 | semidirect |
| 159. #500 | C2×D59 | semidirect |
| 172. #335 | C2×D59 | semidirect |
| 174. C59 | #12372 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D4×D472 | 2 |
| #21426321 | 2 |
| #21426240 | 2 |
| #21422141 | 2 |
| #21422056 | 2 |
| D4⋊(C59⋊C16) | 2 |
| C59×#1675 | 2 |
| #12372 | 59 |