Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
338 conjugacy classes of subgroups; only the 59 normal subgroups are shown.
This group has 338 conjugacy classes of subgroups — too many to draw. Only its 59 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. #21426281 | C2 | semidirect |
| 3. #21426276 | C2 | semidirect |
| 4. #21422110 | C2 | semidirect |
| 5. #21422110 | C2 | semidirect |
| 6. #21422022 | C2 | semidirect |
| 7. C59×#2078 | C2 | semidirect |
| 20. C22⋊(C59⋊C16) | C22 | semidirect |
| 21. C22⋊(C59⋊C16) | C22 | semidirect |
| 22. C2×#107×C59 | C22 | semidirect |
| 26. C59×#341 | C22 | semidirect |
| 160. #2078 | D59 | semidirect |
| 179. C2×#107 | C2×D59 | semidirect |
| 189. #341 | C2×D59 | semidirect |
| 190. C59 | #12284 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21434961 | 2 |
| #21426281 | 2 |
| #21426276 | 2 |
| #21422110 | 2 |
| #21422022 | 2 |
| C59×#2078 | 2 |
| #12284 | 59 |