Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
576 conjugacy classes of subgroups; only the 95 normal subgroups are shown.
This group has 576 conjugacy classes of subgroups — too many to draw. Only its 95 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. #21427253 | C2 | semidirect |
| 3. #21424932 | C2 | semidirect |
| 4. #21422626 | C2 | semidirect |
| 5. #21422001 | C2 | semidirect |
| 6. #21421949 | C2 | semidirect |
| 7. C59×#1507 | C2 | semidirect |
| 10. #16837718 | C4 | semidirect |
| 13. #16837535 | C4 | semidirect |
| 31. C22×D236 | C2×C4 | semidirect |
| 42. C2×C4⋊Dic59 | C2×C4 | semidirect |
| 57. C22⋊(C59⋊C8) | C2×C4 | semidirect |
| 244. #1507 | D59 | semidirect |
| 279. C59 | #9343 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21434893 | 2 |
| #21427253 | 2 |
| #21424932 | 2 |
| #21422626 | 2 |
| #21422001 | 2 |
| #21421949 | 2 |
| C59×#1507 | 2 |
| #9343 | 59 |