Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
512 conjugacy classes of subgroups; only the 75 normal subgroups are shown.
This group has 512 conjugacy classes of subgroups — too many to draw. Only its 75 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×#16837198 | C2 | semidirect |
| 3. #21424500 | C2 | semidirect |
| 4. #21424497 | C2 | semidirect |
| 5. #21424313 | C2 | semidirect |
| 6. #21422222 | C2 | semidirect |
| 7. C2×C59×#355 | C2 | semidirect |
| 77. #101×C59 | D4 | semidirect |
| 233. C2×#355 | D59 | semidirect |
| 266. C59 | #13426 | semidirect |
| 312. #101 | C22⋊D59 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21431120 | 2 |
| C2×#16837198 | 2 |
| #21424500 | 2 |
| #21424497 | 2 |
| #21424313 | 2 |
| #21422222 | 2 |
| C2×C59×#355 | 2 |
| #13426 | 59 |