Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
556 conjugacy classes of subgroups; only the 143 normal subgroups are shown.
This group has 556 conjugacy classes of subgroups — too many to draw. Only its 143 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. #21425671 | C2 | semidirect |
| 2. #21425268 | C2 | semidirect |
| 3. #21425073 | C2 | semidirect |
| 5. #21424338 | C2 | semidirect |
| 35. C4⋊Q8×C59 | Q8 | semidirect |
| 36. #127×C59 | Q8 | semidirect |
| 37. #124×C59 | Q8 | semidirect |
| 140. C59 | #32704 | semidirect |
| 147. C4⋊Q8 | Dic118 | semidirect |
| 148. #127 | Dic118 | semidirect |
| 150. #124 | Dic118 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21425671 | 2 |
| #21425268 | 2 |
| #21425073 | 2 |
| #21424480 | 2 |
| #21424338 | 2 |
| C59×#1962 | 2 |
| #32704 | 59 |