Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
772 conjugacy classes of subgroups; only the 103 normal subgroups are shown.
This group has 772 conjugacy classes of subgroups — too many to draw. Only its 103 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. #21424028 | C2 | semidirect |
| 3. #21424016 | C2 | semidirect |
| 4. #21422639 | C2 | semidirect |
| 5. #21422001 | C2 | semidirect |
| 6. #21421973 | C2 | semidirect |
| 7. C59×#2976 | C2 | semidirect |
| 11. #16837552 | C4 | semidirect |
| 13. #16837535 | C4 | semidirect |
| 267. #2976 | D59 | semidirect |
| 307. C59 | #9520 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21433322 | 2 |
| #21424028 | 2 |
| #21424016 | 2 |
| #21422639 | 2 |
| #21422001 | 2 |
| #21421973 | 2 |
| C59×#2976 | 2 |
| #9520 | 59 |