Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
498 conjugacy classes of subgroups; only the 71 normal subgroups are shown.
This group has 498 conjugacy classes of subgroups — too many to draw. Only its 71 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. #21422688 | C2 | semidirect |
| 3. #21422246 | C2 | semidirect |
| 4. C59×#2126 | C2 | semidirect |
| 5. #16838238 | C4 | semidirect |
| 7. #16837584 | C4 | semidirect |
| 12. #16837386 | C4 | semidirect |
| 15. #16837142 | C22 | semidirect |
| 18. C59×#354 | C22 | semidirect |
| 170. #2126 | D59 | semidirect |
| 190. #354 | C2×D59 | semidirect |
| 194. C59 | #13568 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21433444 | 2 |
| #21422688 | 2 |
| #21422246 | 2 |
| C59×#2126 | 2 |
| #13568 | 59 |