Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
554 conjugacy classes of subgroups; only the 139 normal subgroups are shown.
This group has 554 conjugacy classes of subgroups — too many to draw. Only its 139 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. #21424924 | C2 | semidirect |
| 3. #21422855 | C2 | semidirect |
| 4. #21422548 | C2 | semidirect |
| 5. C42×C8×C59 | C2 | semidirect |
| 7. #16837807 | C4 | semidirect |
| 8. #16837779 | C4 | semidirect |
| 9. #16837749 | C4 | semidirect |
| 67. C42×C59 | D8 | semidirect |
| 104. C8×C59 | #104 | semidirect |
| 125. C42×C8 | D59 | semidirect |
| 147. C59 | #9844 | semidirect |
| 202. C42 | D472 | semidirect |
| 233. C8 | #14273655 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21434675 | 2 |
| #21424924 | 2 |
| #21422855 | 2 |
| #21422548 | 2 |
| C42×C8×C59 | 2 |
| #9844 | 59 |