Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
580 conjugacy classes of subgroups; only the 103 normal subgroups are shown.
This group has 580 conjugacy classes of subgroups — too many to draw. Only its 103 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. C4×#14273642 | C2 | semidirect |
| 3. #21422613 | C2 | semidirect |
| 4. #21421950 | C2 | semidirect |
| 5. C59×#2975 | C2 | semidirect |
| 8. #16837341 | C4 | semidirect |
| 9. #16837338 | C4 | semidirect |
| 10. #16837319 | C4 | semidirect |
| 12. #16837311 | C4 | semidirect |
| 61. C22⋊C8×C59 | D4 | semidirect |
| 196. #2975 | D59 | semidirect |
| 228. C59 | #9186 | semidirect |
| 259. C22⋊C8 | C22⋊D59 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21429980 | 2 |
| C4×#14273642 | 2 |
| #21422613 | 2 |
| #21421950 | 2 |
| C59×#2975 | 2 |
| #9186 | 59 |