Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
716 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 716 conjugacy classes of subgroups — too many to draw. Only its 117 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. #21424414 | C2 | semidirect |
| 2. C2×#16837136 | C2 | semidirect |
| 3. #21422352 | C2 | semidirect |
| 4. #21421939 | C2 | semidirect |
| 31. C59⋊#95 | D4 | semidirect |
| 246. C59 | #10403 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21424414 | 2 |
| C2×#16837136 | 2 |
| #21422352 | 2 |
| #21421939 | 2 |
| C59×#2656 | 2 |
| #10403 | 59 |