Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
628 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 628 conjugacy classes of subgroups — too many to draw. Only its 123 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. C4×#14273642 | C2 | semidirect |
| 4. #21422220 | C2 | semidirect |
| 5. C4×#99×C59 | C2 | semidirect |
| 7. C2×C4×D236 | C4 | semidirect |
| 10. #16837303 | C4 | semidirect |
| 15. #16837267 | C4 | semidirect |
| 17. #16837248 | C4 | semidirect |
| 18. #16837194 | C4 | semidirect |
| 43. #14273642 | C2×C4 | semidirect |
| 61. #99×C59 | C2×C4 | semidirect |
| 95. C2×D236 | C42 | semidirect |
| 119. C4×Dic59 | C42 | semidirect |
| 215. C4×#99 | D59 | semidirect |
| 243. C59 | #12628 | semidirect |
| 276. #99 | C4×D59 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21426818 | 2 |
| C2×#16837194 | 2 |
| C4×#14273642 | 2 |
| #21422220 | 2 |
| C4×#99×C59 | 2 |
| #12628 | 59 |