Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
906 conjugacy classes of subgroups; only the 211 normal subgroups are shown.
This group has 906 conjugacy classes of subgroups — too many to draw. Only its 211 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. #21434671 | C2 | semidirect |
| 2. #21434524 | C2 | semidirect |
| 3. #21423768 | C2 | semidirect |
| 4. #21423765 | C2 | semidirect |
| 5. #21423763 | C2 | semidirect |
| 6. #21423760 | C2 | semidirect |
| 7. C2×#16837123 | C2 | semidirect |
| 8. C59×#3147 | C2 | semidirect |
| 80. C2×C8×C59 | D8 | semidirect |
| 136. #3147 | D59 | semidirect |
| 169. C59 | #19616 | semidirect |
| 225. C2×C8 | #11745669 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21434671 | 2 |
| #21434524 | 2 |
| #21423768 | 2 |
| #21423765 | 2 |
| #21423763 | 2 |
| #21423760 | 2 |
| C2×#16837123 | 2 |
| C59×#3147 | 2 |
| #19616 | 59 |