Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
422 conjugacy classes of subgroups; only the 111 normal subgroups are shown.
This group has 422 conjugacy classes of subgroups — too many to draw. Only its 111 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. C4⋊C16×D59 | C2 | semidirect |
| 3. #346×D59 | C2 | semidirect |
| 4. #21422055 | C2 | semidirect |
| 5. #21422054 | C2 | semidirect |
| 6. #21422053 | C2 | semidirect |
| 7. C59×#1330 | C2 | semidirect |
| 20. C4⋊(C59⋊C16) | C22 | semidirect |
| 22. #16837178 | C22 | semidirect |
| 25. C59×C4⋊C16 | C22 | semidirect |
| 26. C59×#346 | C22 | semidirect |
| 172. #1330 | D59 | direct (N × H) |
| 178. D59 | #1330 | direct (N × H) |
| 194. C4⋊C16 | C2×D59 | semidirect |
| 197. #346 | C2×D59 | semidirect |
| 198. C59 | C2×#1330 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #436×D59 | 2 |
| C4⋊C16×D59 | 2 |
| #346×D59 | 2 |
| #21422055 | 2 |
| #21422054 | 2 |
| #21422053 | 2 |
| C59×#1330 | 2 |
| C2×#1330 | 59 |