Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
690 conjugacy classes of subgroups; only the 211 normal subgroups are shown.
This group has 690 conjugacy classes of subgroups — too many to draw. Only its 211 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. #21423774 | C2 | semidirect |
| 4. #21423770 | C2 | semidirect |
| 57. C2×C8×C59 | Q16 | semidirect |
| 129. C59 | #19618 | semidirect |
| 163. C2×C8 | #11745672 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21434678 | 2 |
| #21434610 | 2 |
| #21423774 | 2 |
| #21423770 | 2 |
| C2×#16837123 | 2 |
| C59×#3160 | 2 |
| #19618 | 59 |