Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
412 conjugacy classes of subgroups; only the 91 normal subgroups are shown.
This group has 412 conjugacy classes of subgroups — too many to draw. Only its 91 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. C2×#16837231 | C2 | semidirect |
| 3. C2×#16837216 | C2 | semidirect |
| 4. C2×#16837202 | C2 | semidirect |
| 5. #21425711 | C2 | semidirect |
| 6. #21424161 | C2 | semidirect |
| 7. C59×#1387 | C2 | semidirect |
| 170. #1387 | D59 | semidirect |
| 195. C59 | #13393 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16837673 | 2 |
| C2×#16837231 | 2 |
| C2×#16837216 | 2 |
| C2×#16837202 | 2 |
| #21425711 | 2 |
| #21424161 | 2 |
| C59×#1387 | 2 |
| #13393 | 59 |