Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
214 conjugacy classes of subgroups; only the 65 normal subgroups are shown.
This group has 214 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. C2×#16837237 | C2 | semidirect |
| 2. C22×C59⋊C32 | C2 | semidirect |
| 3. #21426182 | C2 | semidirect |
| 4. #21422295 | C2 | semidirect |
| 5. #21422274 | C2 | semidirect |
| 6. #21422273 | C2 | semidirect |
| 7. C59×#2215 | C2 | semidirect |
| 28. C59⋊C32 | D4 | semidirect |
| 84. C22×C59 | D32 | semidirect |
| 97. #2215 | D59 | semidirect |
| 120. C59 | #13694 | semidirect |
| 186. C22 | #16837237 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16837237 | 2 |
| C22×C59⋊C32 | 2 |
| #21426182 | 2 |
| #21422295 | 2 |
| #21422274 | 2 |
| #21422273 | 2 |
| C59×#2215 | 2 |
| #13694 | 59 |