Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
610 conjugacy classes of subgroups; only the 203 normal subgroups are shown.
This group has 610 conjugacy classes of subgroups — too many to draw. Only its 203 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×#16837804 | C2 | semidirect |
| 3. #21426328 | C2 | direct (N × H) |
| 4. C2×#16837207 | C2 | semidirect |
| 6. C2×C4×C16×C59 | C2 | semidirect |
| 13. #16837804 | C22 | semidirect |
| 18. #16837207 | C22 | semidirect |
| 22. C4×C16×C59 | C22 | semidirect |
| 121. C2×C4×C16 | D59 | semidirect |
| 122. C2×C59 | #2242 | semidirect |
| 141. C4×C16 | C2×D59 | semidirect |
| 142. C59 | C2×#2242 | semidirect |
| 236. C2 | #21426328 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16837804 | 2 |
| C2×#16837786 | 2 |
| #21426328 | 2 |
| C2×#16837207 | 2 |
| C2×#16837204 | 2 |
| C2×C4×C16×C59 | 2 |
| C2×#2242 | 59 |