Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
558 conjugacy classes of subgroups; only the 83 normal subgroups are shown.
This group has 558 conjugacy classes of subgroups — too many to draw. Only its 83 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 |
|---|---|---|
| 1. #21435226 | C2 | semidirect |
| 3. C2×#16837797 | C2 | semidirect |
| 4. #21422812 | C2 | semidirect |
| 5. #21422708 | C2 | semidirect |
| 6. #21421996 | C2 | semidirect |
| 7. C59×#1469 | C2 | semidirect |
| 188. #1469 | D59 | semidirect |
| 219. C59 | #10132 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21435226 | 2 |
| #21435083 | 2 |
| C2×#16837797 | 2 |
| #21422812 | 2 |
| #21422708 | 2 |
| #21421996 | 2 |
| C59×#1469 | 2 |
| #10132 | 59 |