Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
1030 conjugacy classes of subgroups; only the 267 normal subgroups are shown.
This group has 1030 conjugacy classes of subgroups — too many to draw. Only its 267 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 |
|---|---|---|
| 1. C2×#16837800 | C2 | semidirect |
| 3. C2×#16837775 | C2 | semidirect |
| 4. C2×#16837749 | C2 | semidirect |
| 5. #21423724 | C2 | direct (N × H) |
| 6. C2×C59×#322 | C2 | semidirect |
| 13. #16837800 | C22 | semidirect |
| 17. #16837775 | C22 | semidirect |
| 19. #16837749 | C22 | semidirect |
| 24. C59×#322 | C22 | semidirect |
| 76. C2×C8×C59 | SD16 | semidirect |
| 114. C8×C59 | C2×SD16 | semidirect |
| 135. C2×#322 | D59 | semidirect |
| 136. C2×C59 | #1715 | semidirect |
| 158. #322 | C2×D59 | semidirect |
| 159. C59 | C2×#1715 | semidirect |
| 213. C2×C8 | #11745660 | semidirect |
| 249. C8 | C2×#11745660 | semidirect |
| 266. C2 | #21423724 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16837800 | 2 |
| C2×#16837779 | 2 |
| C2×#16837775 | 2 |
| C2×#16837749 | 2 |
| #21423724 | 2 |
| C2×C59×#322 | 2 |
| C2×#1715 | 59 |