Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
1296 conjugacy classes of subgroups; only the 147 normal subgroups are shown.
This group has 1296 conjugacy classes of subgroups — too many to draw. Only its 147 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. #21424026 | C2 | semidirect |
| 3. C2×#16837126 | C2 | semidirect |
| 4. #21421974 | C2 | semidirect |
| 5. C59×#2315 | C2 | semidirect |
| 12. #16837311 | C4 | semidirect |
| 25. C22×D236 | C2×C4 | semidirect |
| 39. C59⋊#95 | C2×C4 | semidirect |
| 45. C2×C4⋊C4×C59 | D4 | semidirect |
| 135. C23×C59 | #102 | semidirect |
| 234. #2315 | D59 | semidirect |
| 263. C59 | #9017 | semidirect |
| 282. C2×C4⋊C4 | C22⋊D59 | semidirect |
| 402. C23 | #14273647 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16837311 | 2 |
| #21424026 | 2 |
| C2×#16837126 | 2 |
| #21421974 | 2 |
| C59×#2315 | 2 |
| #9017 | 59 |