Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
406 conjugacy classes of subgroups; only the 83 normal subgroups are shown.
This group has 406 conjugacy classes of subgroups — too many to draw. Only its 83 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. #21425894 | C2 | semidirect |
| 3. #21422856 | C2 | semidirect |
| 4. #21422140 | C2 | semidirect |
| 5. #21422139 | C2 | semidirect |
| 6. #21422138 | C2 | semidirect |
| 7. C59×#1360 | C2 | semidirect |
| 19. C4⋊(C59⋊C16) | C22 | semidirect |
| 23. #16837153 | C22 | semidirect |
| 25. C59×C4⋊C16 | C22 | semidirect |
| 26. C59×#334 | C22 | semidirect |
| 177. #1360 | D59 | semidirect |
| 197. C4⋊C16 | C2×D59 | semidirect |
| 202. #334 | C2×D59 | semidirect |
| 203. C59 | #11957 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #495×D59 | 2 |
| #21425894 | 2 |
| #21422856 | 2 |
| #21422140 | 2 |
| #21422139 | 2 |
| #21422138 | 2 |
| C59×#1360 | 2 |
| #11957 | 59 |