Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
882 conjugacy classes of subgroups; only the 197 normal subgroups are shown.
This group has 882 conjugacy classes of subgroups — too many to draw. Only its 197 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. #21424392 | C2 | semidirect |
| 3. #21424392 | C2 | semidirect |
| 4. #21424392 | C2 | semidirect |
| 5. #21424387 | C2 | semidirect |
| 6. #21424241 | C2 | semidirect |
| 7. C59×#1840 | C2 | semidirect |
| 154. #1840 | D59 | semidirect |
| 177. C59 | #23359 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21427377 | 2 |
| #21424392 | 2 |
| #21424387 | 2 |
| #21424241 | 2 |
| C59×#1840 | 2 |
| #23359 | 59 |