Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
288 conjugacy classes of subgroups; only the 59 normal subgroups are shown.
This group has 288 conjugacy classes of subgroups — too many to draw. Only its 59 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 |
|---|---|---|
| 2. C2×#16837239 | C2 | semidirect |
| 3. #21426184 | C2 | semidirect |
| 4. #21422277 | C2 | semidirect |
| 5. #21422275 | C2 | semidirect |
| 6. (C2×D59)⋊C32 | C2 | semidirect |
| 7. C2×C59×Q64 | C2 | semidirect |
| 107. C2×Q64 | D59 | semidirect |
| 133. C59 | #13666 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16837835 | 2 |
| C2×#16837239 | 2 |
| #21426184 | 2 |
| #21422277 | 2 |
| #21422275 | 2 |
| (C2×D59)⋊C32 | 2 |
| C2×C59×Q64 | 2 |
| #13666 | 59 |