Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
170 conjugacy classes of subgroups; only the 55 normal subgroups are shown.
This group has 170 conjugacy classes of subgroups — too many to draw. Only its 55 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. #21422303 | C2 | semidirect |
| 3. #21422285 | C2 | semidirect |
| 4. #21422236 | C2 | semidirect |
| 5. C59×#2161 | C2 | semidirect |
| 70. #2161 | D59 | semidirect |
| 87. C59 | #13717 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21426199 | 2 |
| #21422303 | 2 |
| #21422285 | 2 |
| #21422236 | 2 |
| C59×#2161 | 2 |
| #13717 | 59 |