Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
424 conjugacy classes of subgroups; only the 121 normal subgroups are shown.
This group has 424 conjugacy classes of subgroups — too many to draw. Only its 121 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. #21425884 | C2 | semidirect |
| 4. #21424882 | C2 | semidirect |
| 5. #21422193 | C2 | semidirect |
| 6. #21422186 | C2 | semidirect |
| 25. C59×#361 | C4 | semidirect |
| 59. M32×C59 | C2×C4 | semidirect |
| 62. #108×C59 | C2×C4 | semidirect |
| 182. #361 | Dic59 | semidirect |
| 185. C59 | #12940 | semidirect |
| 205. M32 | C2×Dic59 | semidirect |
| 211. #108 | C2×Dic59 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21432948 | 2 |
| #21425884 | 2 |
| C2×#16837203 | 2 |
| #21424882 | 2 |
| #21422193 | 2 |
| #21422186 | 2 |
| C2×C59×#361 | 2 |
| #12940 | 59 |