Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
390 conjugacy classes of subgroups; only the 87 normal subgroups are shown.
This group has 390 conjugacy classes of subgroups — too many to draw. Only its 87 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. #21425868 | C2 | semidirect |
| 3. C2×#16837219 | C2 | semidirect |
| 4. #21425815 | C2 | semidirect |
| 7. C59×#1384 | C2 | semidirect |
| 161. #1384 | D59 | semidirect |
| 184. C59 | #13397 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21433752 | 2 |
| #21425868 | 2 |
| C2×#16837219 | 2 |
| #21425815 | 2 |
| #21425725 | 2 |
| #21424147 | 2 |
| C59×#1384 | 2 |
| #13397 | 59 |