Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
612 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 612 conjugacy classes of subgroups — too many to draw. Only its 107 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 |
|---|---|---|
| 3. #21425040 | C2 | semidirect |
| 4. #21422609 | C2 | semidirect |
| 5. #21421990 | C2 | semidirect |
| 6. #21421951 | C2 | semidirect |
| 11. #16837682 | C4 | semidirect |
| 12. #16837607 | C4 | semidirect |
| 31. #14273727 | C2×C4 | semidirect |
| 32. #14273727 | C2×C4 | semidirect |
| 46. C4⋊(C59⋊C8) | C2×C4 | semidirect |
| 214. C59 | #9323 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21434195 | 2 |
| #21426457 | 2 |
| #21425040 | 2 |
| #21422609 | 2 |
| #21421990 | 2 |
| #21421951 | 2 |
| C59×#1490 | 2 |
| #9323 | 59 |