Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
378 conjugacy classes of subgroups; only the 109 normal subgroups are shown.
This group has 378 conjugacy classes of subgroups — too many to draw. Only its 109 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. C2×#16837231 | C2 | semidirect |
| 5. #21422211 | C2 | semidirect |
| 6. #21422193 | C2 | semidirect |
| 7. C59×#2161 | C2 | semidirect |
| 18. #16837187 | C4 | semidirect |
| 134. #2161 | D59 | semidirect |
| 161. C59 | #12927 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21432704 | 2 |
| C2×#16837231 | 2 |
| C2×#16837187 | 2 |
| #21424151 | 2 |
| #21422211 | 2 |
| #21422193 | 2 |
| C59×#2161 | 2 |
| #12927 | 59 |