Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
386 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 386 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. #21425843 | C2 | semidirect |
| 3. C2×#16837210 | C2 | semidirect |
| 4. C2×#16837185 | C2 | semidirect |
| 5. #21424143 | C2 | semidirect |
| 6. #21422199 | C2 | semidirect |
| 7. C2×C59×#368 | C2 | semidirect |
| 170. C2×#368 | D59 | semidirect |
| 201. C59 | #13392 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21433817 | 2 |
| #21425843 | 2 |
| C2×#16837210 | 2 |
| C2×#16837185 | 2 |
| #21424143 | 2 |
| #21422199 | 2 |
| C2×C59×#368 | 2 |
| #13392 | 59 |