Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
706 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 706 conjugacy classes of subgroups — too many to draw. Only its 123 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. #21433137 | C2 | semidirect |
| 2. #21424088 | C2 | semidirect |
| 3. #21422764 | C2 | semidirect |
| 4. #21421999 | C2 | semidirect |
| 24. C4⋊(C59⋊C8) | D4 | semidirect |
| 172. C59 | #9405 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21433137 | 2 |
| #21424088 | 2 |
| #21422764 | 2 |
| #21421999 | 2 |
| C59×#2541 | 2 |
| #9405 | 59 |