Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
814 conjugacy classes of subgroups; only the 219 normal subgroups are shown.
This group has 814 conjugacy classes of subgroups — too many to draw. Only its 219 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. #21434656 | C2 | semidirect |
| 3. #21423698 | C2 | semidirect |
| 4. #21423694 | C2 | semidirect |
| 5. #21423689 | C2 | semidirect |
| 6. #21423684 | C2 | semidirect |
| 7. C2×C8×C59⋊C8 | C2 | semidirect |
| 8. C59×#3160 | C2 | semidirect |
| 70. C2×C8×C59 | SD16 | semidirect |
| 109. C59⋊C8 | #135 | semidirect |
| 123. #3160 | D59 | semidirect |
| 156. C59 | #19596 | semidirect |
| 203. C2×C8 | #11745671 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21434656 | 2 |
| #21434524 | 2 |
| #21423698 | 2 |
| #21423694 | 2 |
| #21423689 | 2 |
| #21423684 | 2 |
| C2×C8×C59⋊C8 | 2 |
| C59×#3160 | 2 |
| #19596 | 59 |