Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
462 conjugacy classes of subgroups; only the 97 normal subgroups are shown.
This group has 462 conjugacy classes of subgroups — too many to draw. Only its 97 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×#16837213 | C2 | semidirect |
| 3. #21425809 | C2 | semidirect |
| 4. #21424839 | C2 | semidirect |
| 5. C59×#1377 | C2 | semidirect |
| 45. #14273659 | D4 | semidirect |
| 151. #1377 | D59 | semidirect |
| 172. C59 | #13410 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21434542 | 2 |
| C2×#16837213 | 2 |
| #21425809 | 2 |
| #21424839 | 2 |
| C59×#1377 | 2 |
| #13410 | 59 |