Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
314 conjugacy classes of subgroups; only the 75 normal subgroups are shown.
This group has 314 conjugacy classes of subgroups — too many to draw. Only its 75 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 |
|---|---|---|
| 3. #21422268 | C2 | direct (N × H) |
| 129. C2×C59 | #1413 | semidirect |
| 146. C59 | C2×#1413 | semidirect |
| 251. C2 | #21422268 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16837770 | 2 |
| C2×#16837201 | 2 |
| #21422268 | 2 |
| C2×C59×#356 | 2 |
| C2×#1413 | 59 |