Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
422 conjugacy classes of subgroups; only the 91 normal subgroups are shown.
This group has 422 conjugacy classes of subgroups — too many to draw. Only its 91 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. #21425893 | C2 | semidirect |
| 3. #21422858 | C2 | semidirect |
| 4. #21422058 | C2 | semidirect |
| 5. #21422057 | C2 | semidirect |
| 6. #21422056 | C2 | semidirect |
| 7. C59×#1331 | C2 | semidirect |
| 21. C4×C59⋊C16 | C22 | semidirect |
| 22. #16837155 | C22 | semidirect |
| 25. C4×C16×C59 | C22 | semidirect |
| 26. C59×#335 | C22 | semidirect |
| 171. #1331 | D59 | semidirect |
| 193. C4×C16 | C2×D59 | semidirect |
| 195. #335 | C2×D59 | semidirect |
| 197. C59 | #11661 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×D8×D59 | 2 |
| #21425893 | 2 |
| #21422858 | 2 |
| #21422058 | 2 |
| #21422057 | 2 |
| #21422056 | 2 |
| C59×#1331 | 2 |
| #11661 | 59 |