Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
412 conjugacy classes of subgroups; only the 111 normal subgroups are shown.
This group has 412 conjugacy classes of subgroups — too many to draw. Only its 111 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 |
|---|---|---|
| 4. #21424220 | C2 | semidirect |
| 5. #21422211 | C2 | semidirect |
| 6. #21422198 | C2 | semidirect |
| 7. C59×#2153 | C2 | semidirect |
| 10. #16837515 | C4 | semidirect |
| 134. #2153 | D59 | semidirect |
| 161. C59 | #12826 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21432949 | 2 |
| C2×#16837216 | 2 |
| #21425813 | 2 |
| #21424220 | 2 |
| #21422211 | 2 |
| #21422198 | 2 |
| C59×#2153 | 2 |
| #12826 | 59 |