Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
670 conjugacy classes of subgroups; only the 267 normal subgroups are shown.
This group has 670 conjugacy classes of subgroups — too many to draw. Only its 267 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. #21425967 | C2 | direct (N × H) |
| 18. C2×Q32×C59 | C4 | semidirect |
| 41. Q32×C59 | C2×C4 | semidirect |
| 103. C2×C59 | #2176 | semidirect |
| 108. C2×Q32 | Dic59 | semidirect |
| 120. C59 | C2×#2176 | semidirect |
| 134. Q32 | C2×Dic59 | semidirect |
| 196. C2 | #21425967 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×Q16×Dic59 | 2 |
| #21425967 | 2 |
| C2×#16837230 | 2 |
| C2×#16837206 | 2 |
| C2×#16837177 | 2 |
| C22×Q32×C59 | 2 |
| C2×#2176 | 59 |