Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
556 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 556 conjugacy classes of subgroups — too many to draw. Only its 89 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. #21435479 | C2 | semidirect |
| 3. #21424937 | C2 | semidirect |
| 4. #21422687 | C2 | semidirect |
| 5. #21422517 | C2 | semidirect |
| 6. #21421986 | C2 | semidirect |
| 7. C59×#3138 | C2 | semidirect |
| 189. #3138 | D59 | semidirect |
| 223. C59 | #10112 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21435479 | 2 |
| #21435014 | 2 |
| #21424937 | 2 |
| #21422687 | 2 |
| #21422517 | 2 |
| #21421986 | 2 |
| C59×#3138 | 2 |
| #10112 | 59 |