Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
470 conjugacy classes of subgroups; only the 109 normal subgroups are shown.
This group has 470 conjugacy classes of subgroups — too many to draw. Only its 109 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. #21437198 | C2 | semidirect |
| 3. #21425832 | C2 | semidirect |
| 4. #21424139 | C2 | semidirect |
| 5. #21422202 | C2 | semidirect |
| 6. #21422201 | C2 | semidirect |
| 7. C59×#2145 | C2 | semidirect |
| 14. #16837657 | C4 | semidirect |
| 15. #16837652 | C4 | semidirect |
| 43. #14273667 | D4 | semidirect |
| 65. M32×C59 | D4 | semidirect |
| 179. #2145 | D59 | semidirect |
| 208. C59 | #13077 | semidirect |
| 238. M32 | C22⋊D59 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21437198 | 2 |
| #21433754 | 2 |
| #21425832 | 2 |
| #21424139 | 2 |
| #21422202 | 2 |
| #21422201 | 2 |
| C59×#2145 | 2 |
| #13077 | 59 |