Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
472 conjugacy classes of subgroups; only the 103 normal subgroups are shown.
This group has 472 conjugacy classes of subgroups — too many to draw. Only its 103 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. #21422693 | C2 | semidirect |
| 3. #21422530 | C2 | semidirect |
| 4. #21422449 | C2 | semidirect |
| 5. #21422006 | C2 | semidirect |
| 6. #21421986 | C2 | semidirect |
| 7. C59×#2971 | C2 | semidirect |
| 203. #2971 | D59 | semidirect |
| 240. C59 | #9350 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21433590 | 2 |
| #21422693 | 2 |
| #21422530 | 2 |
| #21422449 | 2 |
| #21422006 | 2 |
| #21421986 | 2 |
| C59×#2971 | 2 |
| #9350 | 59 |