Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
456 conjugacy classes of subgroups; only the 95 normal subgroups are shown.
This group has 456 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 |
|---|---|---|
| 3. #21422699 | C2 | semidirect |
| 5. #21422453 | C2 | semidirect |
| 6. #21421946 | C2 | semidirect |
| 7. C59×#1290 | C2 | semidirect |
| 202. #1290 | D59 | semidirect |
| 236. C59 | #9245 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16837703 | 2 |
| #21433133 | 2 |
| #21422699 | 2 |
| #21422538 | 2 |
| #21422453 | 2 |
| #21421946 | 2 |
| C59×#1290 | 2 |
| #9245 | 59 |