Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
474 conjugacy classes of subgroups; only the 109 normal subgroups are shown.
This group has 474 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 |
|---|---|---|
| 4. C2×#16837206 | C2 | semidirect |
| 5. #21422206 | C2 | semidirect |
| 6. #21422185 | C2 | semidirect |
| 7. C59×#1979 | C2 | semidirect |
| 11. #16837843 | C4 | semidirect |
| 45. #14273667 | C2×C4 | semidirect |
| 60. C2×Q16×C59 | C2×C4 | semidirect |
| 180. #1979 | D59 | semidirect |
| 209. C59 | #13023 | semidirect |
| 222. C2×Q16 | C4×D59 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16837843 | 2 |
| #21432973 | 2 |
| C2×#16837208 | 2 |
| C2×#16837206 | 2 |
| #21422206 | 2 |
| #21422185 | 2 |
| C59×#1979 | 2 |
| #13023 | 59 |