Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
492 conjugacy classes of subgroups; only the 109 normal subgroups are shown.
This group has 492 conjugacy classes of subgroups — too many to draw. Only its 109 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. #21432704 | C2 | semidirect |
| 3. C2×#16837215 | C2 | semidirect |
| 4. #21425725 | C2 | semidirect |
| 5. #21422209 | C2 | semidirect |
| 6. #21422200 | C2 | semidirect |
| 7. C2×C59×#361 | C2 | semidirect |
| 166. C2×#361 | D59 | semidirect |
| 194. C59 | #13007 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16837669 | 2 |
| #21432704 | 2 |
| C2×#16837215 | 2 |
| #21425725 | 2 |
| #21422209 | 2 |
| #21422200 | 2 |
| C2×C59×#361 | 2 |
| #13007 | 59 |