Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
176 conjugacy classes of subgroups; only the 57 normal subgroups are shown.
This group has 176 conjugacy classes of subgroups — too many to draw. Only its 57 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. #21426370 | C2 | semidirect |
| 3. #21422297 | C2 | semidirect |
| 4. Dic59⋊C32 | C2 | semidirect |
| 7. C59×#1424 | C2 | semidirect |
| 23. D944 | Q8 | semidirect |
| 79. #1424 | D59 | semidirect |
| 98. C59 | #13705 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21426370 | 2 |
| #21425942 | 2 |
| #21422297 | 2 |
| Dic59⋊C32 | 2 |
| #21422275 | 2 |
| #21422273 | 2 |
| C59×#1424 | 2 |
| #13705 | 59 |