Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
532 conjugacy classes of subgroups; only the 83 normal subgroups are shown.
This group has 532 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 |
|---|---|---|
| 2. C4×#14273642 | C2 | semidirect |
| 3. #21422097 | C2 | semidirect |
| 4. #21422094 | C2 | semidirect |
| 5. C59×#1466 | C2 | semidirect |
| 6. C2×#14273701 | C4 | semidirect |
| 9. #16837332 | C4 | semidirect |
| 11. #16837319 | C4 | semidirect |
| 17. C2×C59⋊#95 | C4 | semidirect |
| 194. #1466 | D59 | semidirect |
| 222. C59 | #11775 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21429052 | 2 |
| C4×#14273642 | 2 |
| #21422097 | 2 |
| #21422094 | 2 |
| C59×#1466 | 2 |
| #11775 | 59 |