Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
216 conjugacy classes of subgroups; only the 61 normal subgroups are shown.
This group has 216 conjugacy classes of subgroups — too many to draw. Only its 61 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×#16837241 | C2 | semidirect |
| 3. #21426357 | C2 | semidirect |
| 4. C4×D944 | C2 | semidirect |
| 5. #21422278 | C2 | semidirect |
| 6. #21422275 | C2 | semidirect |
| 7. C59×C4⋊C32 | C2 | semidirect |
| 97. C4⋊C32 | D59 | semidirect |
| 118. C59 | #13689 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16837241 | 2 |
| C2×D1888 | 2 |
| #21426357 | 2 |
| C4×D944 | 2 |
| #21422278 | 2 |
| #21422275 | 2 |
| C59×C4⋊C32 | 2 |
| #13689 | 59 |