Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
176 conjugacy classes of subgroups; only the 65 normal subgroups are shown.
This group has 176 conjugacy classes of subgroups — too many to draw. Only its 65 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. #21426371 | C2 | semidirect |
| 3. #21422298 | C2 | semidirect |
| 5. C59×C4⋊C32 | C2 | semidirect |
| 19. D944 | Q8 | semidirect |
| 70. C4⋊C32 | D59 | semidirect |
| 85. C59 | #13705 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21426371 | 2 |
| C4×D944 | 2 |
| #21422298 | 2 |
| #21422275 | 2 |
| C59×C4⋊C32 | 2 |
| #13705 | 59 |