Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
552 conjugacy classes of subgroups; only the 101 normal subgroups are shown.
This group has 552 conjugacy classes of subgroups — too many to draw. Only its 101 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. #21437230 | C2 | semidirect |
| 2. #21425824 | C2 | semidirect |
| 3. #21424989 | C2 | semidirect |
| 4. #21422176 | C2 | semidirect |
| 5. C59×#3150 | C2 | semidirect |
| 26. C2×Dic236 | D4 | semidirect |
| 28. C2×D472 | D4 | semidirect |
| 36. C2×C59⋊C16 | D4 | semidirect |
| 159. #3150 | D59 | semidirect |
| 186. C59 | #13340 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21437230 | 2 |
| #21425824 | 2 |
| #21424989 | 2 |
| #21422176 | 2 |
| C59×#3150 | 2 |
| #13340 | 59 |