Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
498 conjugacy classes of subgroups; only the 81 normal subgroups are shown.
This group has 498 conjugacy classes of subgroups — too many to draw. Only its 81 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. #21435294 | C2 | semidirect |
| 3. #21422730 | C2 | semidirect |
| 4. #21422569 | C2 | semidirect |
| 5. #21422437 | C2 | semidirect |
| 6. #21421957 | C2 | semidirect |
| 7. C59×#3110 | C2 | semidirect |
| 191. #3110 | D59 | semidirect |
| 228. C59 | #10042 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21435294 | 2 |
| #21434096 | 2 |
| #21422730 | 2 |
| #21422569 | 2 |
| #21422437 | 2 |
| #21421957 | 2 |
| C59×#3110 | 2 |
| #10042 | 59 |