Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
572 conjugacy classes of subgroups; only the 139 normal subgroups are shown.
This group has 572 conjugacy classes of subgroups — too many to draw. Only its 139 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×#16837211 | C2 | semidirect |
| 3. #21425707 | C2 | semidirect |
| 4. #21422203 | C2 | semidirect |
| 5. C22×#106×C59 | C2 | semidirect |
| 9. #16837643 | C4 | semidirect |
| 10. #16837638 | C4 | semidirect |
| 24. C2×Dic236 | C2×C4 | semidirect |
| 26. C2×D472 | C2×C4 | semidirect |
| 36. #14273661 | C2×C4 | semidirect |
| 54. #106×C59 | D4 | semidirect |
| 140. C22×C59 | #360 | semidirect |
| 155. C22×#106 | D59 | semidirect |
| 180. C59 | #13001 | semidirect |
| 212. #106 | C22⋊D59 | semidirect |
| 301. C22 | #16837211 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21433677 | 2 |
| C2×#16837211 | 2 |
| #21425707 | 2 |
| #21422203 | 2 |
| C22×#106×C59 | 2 |
| #13001 | 59 |