Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
690 conjugacy classes of subgroups; only the 95 normal subgroups are shown.
This group has 690 conjugacy classes of subgroups — too many to draw. Only its 95 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. #21433124 | C2 | semidirect |
| 3. #21422810 | C2 | semidirect |
| 4. #21422436 | C2 | semidirect |
| 5. #21421953 | C2 | semidirect |
| 6. #21421951 | C2 | semidirect |
| 7. C59×#1555 | C2 | semidirect |
| 51. C4⋊(C59⋊C8) | D4 | semidirect |
| 68. C4⋊C8×C59 | D4 | semidirect |
| 217. #1555 | D59 | semidirect |
| 250. C59 | #9457 | semidirect |
| 283. C4⋊C8 | C22⋊D59 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21433124 | 2 |
| #21429043 | 2 |
| #21422810 | 2 |
| #21422436 | 2 |
| #21421953 | 2 |
| #21421951 | 2 |
| C59×#1555 | 2 |
| #9457 | 59 |