Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
290 conjugacy classes of subgroups; only the 103 normal subgroups are shown.
This group has 290 conjugacy classes of subgroups — too many to draw. Only its 103 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×#16837232 | C2 | semidirect |
| 3. #21422281 | C2 | semidirect |
| 4. C2×C59×M64 | C2 | semidirect |
| 15. #16837232 | C22 | semidirect |
| 19. C2×C32×C59 | C22 | semidirect |
| 108. C2×M64 | D59 | semidirect |
| 128. C2×C32 | C2×D59 | semidirect |
| 131. C59 | #13620 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16837834 | 2 |
| C2×#16837232 | 2 |
| #21422281 | 2 |
| C2×C59×M64 | 2 |
| #13620 | 59 |