Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
444 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 444 conjugacy classes of subgroups — too many to draw. Only its 89 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. #21424231 | C2 | semidirect |
| 4. C2×#16837144 | C2 | semidirect |
| 6. #21421978 | C2 | semidirect |
| 7. C59×#1992 | C2 | semidirect |
| 200. #1992 | D59 | semidirect |
| 235. C59 | #10426 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21432146 | 2 |
| #21424910 | 2 |
| #21424231 | 2 |
| C2×#16837144 | 2 |
| C2×#16837141 | 2 |
| #21421978 | 2 |
| C59×#1992 | 2 |
| #10426 | 59 |