Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
418 conjugacy classes of subgroups; only the 79 normal subgroups are shown.
This group has 418 conjugacy classes of subgroups — too many to draw. Only its 79 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. #21426319 | C2 | semidirect |
| 2. #21426243 | C2 | semidirect |
| 3. #21423495 | C2 | semidirect |
| 4. #21422142 | C2 | semidirect |
| 5. #21422057 | C2 | semidirect |
| 6. D4⋊(C59⋊C16) | C2 | semidirect |
| 8. #16837807 | C22 | semidirect |
| 11. C4⋊(C59⋊C16) | C22 | semidirect |
| 14. C4×C59⋊C16 | C22 | semidirect |
| 15. #16837155 | C22 | semidirect |
| 174. C59 | #12372 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21426319 | 2 |
| #21426243 | 2 |
| #21423495 | 2 |
| #21422142 | 2 |
| #21422057 | 2 |
| D4⋊(C59⋊C16) | 2 |
| D4×D8×C59 | 2 |
| #12372 | 59 |