Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
226 conjugacy classes of subgroups; only the 77 normal subgroups are shown.
This group has 226 conjugacy classes of subgroups — too many to draw. Only its 77 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. #21423010 | C2 | semidirect |
| 2. #21422162 | C2 | semidirect |
| 3. #21422063 | C2 | semidirect |
| 4. #21422016 | C2 | semidirect |
| 42. C16×C59 | M16 | semidirect |
| 84. C59 | #12089 | semidirect |
| 112. C16 | #11745664 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21423010 | 2 |
| #21422162 | 2 |
| #21422063 | 2 |
| #21422016 | 2 |
| C59×#2177 | 2 |
| #12089 | 59 |