Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
624 conjugacy classes of subgroups; only the 127 normal subgroups are shown.
This group has 624 conjugacy classes of subgroups — too many to draw. Only its 127 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. #21432660 | C2 | semidirect |
| 3. #21422763 | C2 | semidirect |
| 4. #21421955 | C2 | semidirect |
| 5. C59×#1458 | C2 | semidirect |
| 42. C4⋊(C59⋊C8) | D4 | semidirect |
| 181. #1458 | D59 | semidirect |
| 207. C59 | #9197 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21432660 | 2 |
| #21429846 | 2 |
| #21422763 | 2 |
| #21421955 | 2 |
| C59×#1458 | 2 |
| #9197 | 59 |