Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
578 conjugacy classes of subgroups; only the 155 normal subgroups are shown.
This group has 578 conjugacy classes of subgroups — too many to draw. Only its 155 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. #21426343 | C2 | semidirect |
| 4. #21426342 | C2 | semidirect |
| 5. #21426341 | C2 | semidirect |
| 6. #21426322 | C2 | semidirect |
| 9. C59×#2245 | C2 | semidirect |
| 148. #2245 | D59 | semidirect |
| 180. C59 | #33705 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21434609 | 2 |
| #494×D59 | 2 |
| #21426343 | 2 |
| #21426342 | 2 |
| #21426341 | 2 |
| #21426322 | 2 |
| #21425814 | 2 |
| #21425689 | 2 |
| C59×#2245 | 2 |
| #33705 | 59 |