Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
418 conjugacy classes of subgroups; only the 109 normal subgroups are shown.
This group has 418 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 |
| 3. C2×#16837210 | C2 | semidirect |
| 4. C2×#16837177 | C2 | semidirect |
| 5. #21424985 | C2 | semidirect |
| 6. #21424982 | C2 | semidirect |
| 7. C2×C59×#359 | C2 | semidirect |
| 11. C2×#14273673 | C4 | semidirect |
| 12. C2×#14273671 | C4 | semidirect |
| 13. C2×#14273670 | C4 | semidirect |
| 14. C2×#14273668 | C4 | semidirect |
| 176. C2×#359 | D59 | semidirect |
| 207. C59 | #13242 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16837832 | 2 |
| C2×#16837231 | 2 |
| C2×#16837210 | 2 |
| C2×#16837177 | 2 |
| #21424985 | 2 |
| #21424982 | 2 |
| C2×C59×#359 | 2 |
| #13242 | 59 |