Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
1026 conjugacy classes of subgroups; only the 119 normal subgroups are shown.
This group has 1026 conjugacy classes of subgroups — too many to draw. Only its 119 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 |
|---|---|---|
| 2. #21424895 | C2 | semidirect |
| 3. #21422792 | C2 | semidirect |
| 4. #21422708 | C2 | semidirect |
| 5. C59×#1466 | C2 | semidirect |
| 14. C2×C4⋊(C59⋊C8) | C22 | semidirect |
| 16. C2×#14273638 | C22 | semidirect |
| 21. C59×#432 | C22 | semidirect |
| 167. #1466 | D59 | semidirect |
| 183. #432 | C2×D59 | semidirect |
| 191. C59 | #8456 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21437860 | 2 |
| #21424895 | 2 |
| #21422792 | 2 |
| #21422708 | 2 |
| C59×#1466 | 2 |
| #8456 | 59 |