Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
398 conjugacy classes of subgroups; only the 95 normal subgroups are shown.
This group has 398 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. C2×#16837219 | C2 | semidirect |
| 4. #21425011 | C2 | semidirect |
| 6. #21422190 | C2 | semidirect |
| 7. C59×#2151 | C2 | semidirect |
| 150. #2151 | D59 | semidirect |
| 178. C59 | #13440 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#14273672 | 2 |
| C2×#16837219 | 2 |
| C2×#16837216 | 2 |
| #21425011 | 2 |
| #21425006 | 2 |
| #21422190 | 2 |
| C59×#2151 | 2 |
| #13440 | 59 |