Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
350 conjugacy classes of subgroups; only the 111 normal subgroups are shown.
This group has 350 conjugacy classes of subgroups — too many to draw. Only its 111 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. #21425899 | C2 | semidirect |
| 2. C2×#16837155 | C2 | semidirect |
| 3. #21422154 | C2 | semidirect |
| 4. #21422142 | C2 | semidirect |
| 144. C59 | #11952 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21425899 | 2 |
| C2×#16837155 | 2 |
| #21422154 | 2 |
| #21422142 | 2 |
| C59×#3169 | 2 |
| #11952 | 59 |