Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
1190 conjugacy classes of subgroups; only the 171 normal subgroups are shown.
This group has 1190 conjugacy classes of subgroups — too many to draw. Only its 171 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. C2×#16837204 | C2 | semidirect |
| 3. #21424125 | C2 | semidirect |
| 4. C2×C59×C22⋊C16 | C2 | semidirect |
| 9. C22×D472 | C4 | semidirect |
| 11. C2×#14273661 | C22 | semidirect |
| 16. C22×C16×C59 | C22 | semidirect |
| 81. D472 | C22⋊C4 | semidirect |
| 123. C22×C59 | #357 | semidirect |
| 142. C2×C22⋊C16 | D59 | semidirect |
| 158. C22×C16 | C2×D59 | semidirect |
| 164. C59 | #12731 | semidirect |
| 275. C22 | #16837204 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×D472 | 2 |
| C2×#16837204 | 2 |
| #21424125 | 2 |
| C2×C59×C22⋊C16 | 2 |
| #12731 | 59 |