Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
390 conjugacy classes of subgroups; only the 91 normal subgroups are shown.
This group has 390 conjugacy classes of subgroups — too many to draw. Only its 91 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. #21425869 | C2 | semidirect |
| 3. #21425833 | C2 | semidirect |
| 4. #21425804 | C2 | semidirect |
| 5. #21424142 | C2 | semidirect |
| 6. #21422192 | C2 | semidirect |
| 7. C2×C59×#350 | C2 | semidirect |
| 174. C2×#350 | 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 |
| #21425869 | 2 |
| #21425833 | 2 |
| #21425804 | 2 |
| #21424142 | 2 |
| #21422192 | 2 |
| C2×C59×#350 | 2 |
| #13401 | 59 |