Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
626 conjugacy classes of subgroups; only the 201 normal subgroups are shown.
This group has 626 conjugacy classes of subgroups — too many to draw. Only its 201 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. #21424813 | C2 | semidirect |
| 4. #21424656 | C2 | semidirect |
| 6. #21424250 | C2 | semidirect |
| 7. C59×#1840 | C2 | semidirect |
| 118. #1840 | D59 | semidirect |
| 140. C59 | #23381 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21427394 | 2 |
| #21424813 | 2 |
| #21424703 | 2 |
| #21424656 | 2 |
| #21424280 | 2 |
| #21424250 | 2 |
| C59×#1840 | 2 |
| #23381 | 59 |