Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
856 conjugacy classes of subgroups; only the 103 normal subgroups are shown.
This group has 856 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. #21425781 | C2 | semidirect |
| 3. #21425745 | C2 | semidirect |
| 4. #21424643 | C2 | semidirect |
| 5. C59×#1884 | C2 | semidirect |
| 7. #16838144 | C4 | semidirect |
| 11. #16838037 | C4 | semidirect |
| 16. #16837386 | C22 | semidirect |
| 22. C59×#568 | C22 | semidirect |
| 25. C59×#410 | C22 | semidirect |
| 205. #1884 | D59 | semidirect |
| 212. #568 | C2×D59 | semidirect |
| 227. #410 | C2×D59 | semidirect |
| 233. C59 | #12769 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21438501 | 2 |
| #21425781 | 2 |
| #21425745 | 2 |
| #21424643 | 2 |
| C59×#1884 | 2 |
| #12769 | 59 |