Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
390 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 390 conjugacy classes of subgroups — too many to draw. Only its 89 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. #21425831 | C2 | semidirect |
| 4. #21425801 | C2 | semidirect |
| 5. C2×#16837186 | C2 | semidirect |
| 6. #21422191 | C2 | semidirect |
| 7. C59×#1812 | C2 | semidirect |
| 175. #1812 | D59 | semidirect |
| 202. C59 | #13401 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21433816 | 2 |
| #21425868 | 2 |
| #21425831 | 2 |
| #21425801 | 2 |
| C2×#16837186 | 2 |
| #21422191 | 2 |
| C59×#1812 | 2 |
| #13401 | 59 |